We study the existence and asymptotic behavior of least energy sign-changing solutions for a N-Laplacian equation of Kirchhoff type with critical exponential growth in \(\mathbb {R}^N\)$$\begin{aligned} \left\{ \begin{aligned}&- \bigg (a+b\int _{\mathbb {R}^N}|\nabla u|^N\mathrm{d}x\bigg )\Delta _N u+V(|x|) |u|^{N-2}u= f(|x|,u), \\&u\in W^{1,N}(\mathbb {R}^N), \\ \end{aligned} \right. \end{aligned}$$

In this paper, we give some vanishing theorems for harmonic p-forms on complete noncompact Riemannian manifolds satisfying a weighted p-Poincaré inequality with nonnegative scalar curvature and under pointwise curvature pinching conditions which are bounded from above by the weight function.

This paper investigates the nonlinear backward fractional diffusion equations (BFDEs) having a variable order and variable diffusion coefficient. It is well-known that the BFDEs are ill-posed in the sense of Hadamard. Moreover, we investigate the problem taking into account the disturbance both variable diffusion coefficient and variable order. This may lead to some common regularization strategy to

The commuting graph \(\varDelta (G)\) of a finite non-abelian group G is a simple graph with vertex set G, and two distinct vertices x, y are adjacent if \(xy = yx\). In this paper, first we discuss some properties of \(\varDelta (G)\). We determine the edge connectivity and the minimum degree of \(\varDelta (G)\) and prove that both are equal. Then, other graph invariants, namely: matching number

In this work, we look at the extension of classical discrete dynamical system to multidimensional discrete-time dynamical system by characterizing chaos notions on \({\mathbb {Z}}^d\)-action. The \({\mathbb {Z}}^d\)-action on a space X has been defined in a very general manner, and therefore we introduce a \({\mathbb {Z}}^d\)-action on X which is induced by a continuous map, \(f:{\mathbb {Z}}\times

The paper proposes a new explicit extragradient algorithm for solving an equilibrium problem over the solution set of another generalized equilibrium problem which usually is called bilevel equilibrium problems in a real Hilbert space. The algorithm combines extragradient methods with auxiliary problem techniques. Theorem of the strong convergence of the algorithm is established under standard assumptions

The key goal of this article is to propose a modification of certain exponential type operators defined by Ismail and May. Particularly, we concentrate on a sequence of operators that preserve \(e^{-x}\) and constant functions. We find the moments of these modified operators using the concept of moment generating function with the help of Mathematica software. We show uniform convergence of these modified

The independence polynomial of a graph G is \(I(G;x)=\sum _{k=0}^{\alpha (G)} s_{k}\cdot x^{k}\), where \(s_{k}\) and \(\alpha (G)\) denote the number of independent sets of cardinality k and the independence number of G, respectively. We say that a cycle is a \(\tilde{3}\)-cycle if its length is divisible by 3, otherwise a non-\(\tilde{3}\)-cycle. Define \(\phi (G)\) to be the decycling number of

In the present work, we investigate infinite horizon optimal control problems driven by a class of stochastic delay evolution equations in Hilbert spaces and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation (ABSEE). We first establish a priori estimate for the solution to ABSEEs by imposing restriction on unbounded operator \(A^*\), that is, the operator

We consider almost Riemann solitons \((V,\lambda )\) in a Riemannian manifold and underline their relation to almost Ricci solitons. When V is of gradient type, using Bochner formula, we explicitly express the function \(\lambda \) by means of the gradient vector field V and illustrate the result with suitable examples. Moreover, we deduce some properties for the particular cases when the potential

In the present work, we investigate the global existence and uniform decay rates of solutions to the Cauchy problem in \(\mathbf {R}^{n}\) (\(n\ge 1)\) related to the dynamic behavior of evolution equations accounting for rotational inertial forces along with a linear viscoelastic memory damping arising in viscoelastic materials. Under certain conditions on the initial data and on the kernel, the global

Let \(\mathcal {L}_2=(-\Delta )^2+V^2 \) be the Schrödinger-type operator on \(\mathbb {R}^n (n\ge 5),\) where the nonnegative potential \(V\) belongs to the reverse Hölder class \(RH_s, n/2

In this paper, we study the concomitants of m-generalized order statistics (m-GOSs) and m-dual generalized order statistics (m-DGOSs) from bivariate Cambanis family with nonzero parameter values as an extension of several recent papers. Moreover, we derive some information measures, namely the Shannon entropy, Kullback–Leibler (KL) divergence and Fisher information number (FIN) for the concomitants

We consider discrete Sturm–Liouville-type equations of the form $$\begin{aligned} \varDelta (r_n\varDelta x_n)=a_nf(x_{\sigma (n)})+b_n. \end{aligned}$$ We present a theory of asymptotic properties of solutions which allows us to control the degree of approximation. Namely, we establish conditions under which for a given sequence y which solves the equation \(\varDelta (r_n\varDelta y_n)=b_n\), the

We define and analyze the k-directional short-time Fourier transform and its synthesis operator over Gelfand–Shilov spaces \(\mathcal {S}^\alpha _{\beta }(\mathbb {R}^n)\) and \(\mathcal {S}^\alpha _{\beta }({\mathbb {R}}^{k+n})\), respectively, and their duals. Also, we investigate directional regular sets and their complements—directional wave fronts, for elements of \(\mathcal {S}^{\prime \alpha

We consider a reaction–diffusion equation on a 3D thin porous media of thickness \(\varepsilon \) which is perforated by periodically distributed cylinders of size \(\varepsilon \). On the boundary of the cylinders, we prescribe a dynamical boundary condition of pure-reactive type. As \(\varepsilon \rightarrow 0\), in the 2D limit the resulting reaction–diffusion equation has a source term coming from

In this paper, we prove that if a nonconstant finite order meromorphic function f and its n-th order difference operator \(\Delta ^n_{\eta }f\) share \(a_1,\) \(a_2,\) \(a_3\) CM, where n is a positive integer, \(\eta \ne 0\) is a finite complex value, and \(a_1,\) \(a_2,\) \(a_3\) are three distinct finite complex values, then \(f(z)=\Delta ^n_{\eta }f(z)\) for each \(z\in \mathbb {C}.\) The main

In this paper, we present some new identities for multiple polylogarithm functions by using the methods of iterated integral computations of logarithm functions. Then, by applying these formulas obtained, we establish several duality formulas for Arakawa–Kaneko zeta values and Kaneko–Tsumura \(\eta \)-values. At the end of the paper, we study a variant of Kaneko–Tsumura \(\eta \)-function with r-complex

We study hypersurfaces in the pseudo-Euclidean space, whose mean curvature vector satisfies the equation: Laplacian of the vector is parallel to the vector (with constant factor), and the second fundamental form has constant norm. We prove that every such hypersurface of diagonalizable shape operator with at most six distinct principal curvatures has constant mean curvature and constant scalar curvature

The class of \(\{P_1,P_2\}\)-Nekrasov matrices, defined in terms of permutation matrices \(P_1\) and \(P_2\), is a generalization of the well-known class of Nekrasov matrices. In this paper, some computable error bounds for linear complementarity problems (LCPs) of \(\{P_1,P_2\}\)-Nekrasov matrices are given, which depend only on the entries of the involved matrices and can be used to obtain the perturbation

For a connected graph G and \(a,b \in \mathbb {R}\), the general degree-eccentricity index is defined as \(\mathrm{DEI}_{a,b}(G) = \sum _{v \in V(G)} d_{G}^{a}(v) \mathrm{ecc}_{G}^{b}(v)\), where V(G) is the vertex set of G, \(d_{G} (v)\) is the degree of a vertex v and \(\mathrm{ecc}_{G}(v)\) is the eccentricity of v in G. We obtain sharp upper and lower bounds on the general degree-eccentricity index

In this paper, an SEIRS epidemic model is proposed, incorporating appropriate compartments as isolated exposed class and diagnosed class, relevant to interventions. In the scenario of constant isolated proportion, the qualitative analyses are carried out in terms of the basic reproduction number \(\mathscr {R}_0\). The sensitivity of \(\mathscr {R}_0\) with respect to model parameters is discussed

Let R be a noncommutative prime ring of characteristic different from 2 and 3, C the extended centroid of R, F and G two generalized derivations of R, d a nonzero derivation of R and \(f(x_1,\ldots ,x_n)\) a multilinear polynomial over C. Suppose that I is a nonzero ideal of R and \(f(I)=\{f(x_1,\ldots ,x_n)| x_1,\ldots ,x_n\in I\}\). If \(f(x_1,\ldots ,x_n)\) is not central valued on R and $$\begin{aligned}

The Bohr radius for a class \({\mathcal {G}}\) consisting of analytic functions \(f(z)=\sum _{n=0}^{\infty }a_nz^n\) in unit disc \({\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1\}\) is the largest \(r^*\) such that every function f in the class \({\mathcal {G}}\) satisfies the inequality $$\begin{aligned} d\left( \sum _{n=0}^{\infty }|a_nz^n|, |f(0)|\right) = \sum _{n=1}^{\infty }|a_nz^n|\le d(f(0), \partial

The aim of this paper is to show that fixed point theorem in cones can be applied to singular equations. Using the positivity of Green’s function and the external force e(t), we prove the existence of a positive periodic solution for a damped singular equation with sub-linearity, semi-linearity and super-linearity conditions, and these results are applicable to weak and strong singularities. As applications

In this paper, the products of modified Bessel functions of the first kind are considered. Our main aim is to provide various conditions so that these products have certain geometric properties such as starlikeness, convexity, and close to convexity (univalency) with respect to certain functions in the unit disk. Subordinating factor sequences for these products are also obtained. Interesting consequences

In this paper, we prove global existence of strong solutions to the 2D density-dependent incompressible magnetic Bénard problem in a bounded domain.

In this work, we estimate the bounds for the logarithmic coefficients \(\gamma _n\) of some well-known classes like \({\mathcal {F}}(c)\) for \(c\in (0,0.656]\cup \{2\}\). The best bound obtained for the logarithmic coefficient \(|\gamma _5|\) is sharp for \(c=2\). In a special case, it is important to note that we obtain the bounds for the logarithmic coefficients \(\gamma _n\) of the convex functions

In 2011, Gross derived an \(O(n^2)\)-time algorithm to calculate the genus distribution of a given cubic Halin graph. In this paper, with the help of the overlap matrix, we obtain a recurrence relation for the Euler-genus polynomials of cubic caterpillar-Halin graphs. Explicit formulas for the embeddings of the cubic caterpillar-Halin graphs into surfaces with Euler-genus 0, 1 and 2 are also obtained

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if \(\beta (G)\) denotes the metric dimension of a maximal outerplanar graph G of order n, we prove that \(2\le \beta (G) \le \lceil \frac{2n}{5}\rceil \) and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of G is 2 and to build a resolving set S of size

The present paper deals with a generalization of the Baskakov type operators, which preserve an exponential function and approximate functions with arbitrary order. We give some direct results including error estimation and quantitative asymptotic formula. It is observed that the rate of approximation can be made smaller by arbitrarily chosen sequences.

In this paper, we study ad-nilpotent elements in Lie algebras arising from semiprime associative rings R free of 2-torsion. With the idea of keeping under control the torsion of R, we introduce a more restrictive notion of ad-nilpotent element, pure ad-nilpotent element, which is a only technical condition since every ad-nilpotent element can be expressed as an orthogonal sum of pure ad-nilpotent elements

The aim of this paper is to complement existing oscillation results for third-order neutral advanced differential equations under the condition of \(\gamma >0\); in particular, the sufficient conditions are given in different way when \(\gamma =1\). Our main idea is by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Then, combining with the results which guarantee

To produce more flexible model, the Bayesian and classical inference of the stress–strength parameter, R, is studied under Type-II progressive censored samples, when stress and strength are two independent Weibull-half-logistic variables. In classical inference, the maximum likelihood estimation, approximation maximum likelihood estimation, uniformly minimum variance unbiased estimate and asymptotic

For a connected graph G(V, E), a vertex \(w\in V(G)\) strongly resolves two vertices \(u, v \in V(G)\) if there exists a shortest \(u-w\) path containing v or a shortest \(v-w\) path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric

For an edge-colored graph G, a set F of edges of G is called a proper edge-cut if F is an edge-cut of G and any pair of adjacent edges in F are assigned different colors. An edge-colored graph is proper disconnected if for each pair of distinct vertices of G there exists a proper edge-cut separating them. For a connected graph G, the proper disconnection number of G, denoted by pd(G), is the minimum

In this paper, we mainly study the geometric model of the derived category of gentle one-cycle algebras provided by Opper, Plamondon and Schroll. We provide a realization of AAG-invariant on the surface, which is slightly different from the realization in their paper, and deduce a standard form of marked surfaces of gentle one-cycle algebras under derived equivalences. As an application, we classify

Due to the Nevanlinna theory, the paper gives the general structure of transcendental meromorphic solutions of a certain ordinary differential equation with rational coefficients. As an application, the meromorphic solutions of the FitzHugh–Nagumo system are obtained in explicit form.

In this paper, we obtain error bound for pseudo-binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein’s method. We also discuss approximation results for weighted sums of independent random variables. We demonstrate our results through some applications in finance and runs in statistics.

The notion of R-dual in general Hilbert spaces was first introduced by Casazza et al. (J Fourier Anal Appl 10:383–408, 2004), with the motivation to obtain a general version of the duality principle in Gabor analysis. On the other hand, the space \(L^2({{\mathbb {R}}}_+)\) of square integrable functions on the half real line \({\mathbb {R}}_{+}\) admits no traditional wavelet or Gabor frame due to

We consider two types of continued fraction expansions of the generating functions of Cauchy numbers. One type has been often studied by many authors, but another has not. In this paper, we give several continued fraction expansions of hypergeometric Cauchy numbers, shifted Cauchy numbers and leaping Cauchy numbers. In special cases, continued fraction expansions of the classical Cauchy numbers of

We call the solution of a kind of weighted Laplace equation complex-valued kernel \(\alpha \)-harmonic mappings. In this paper, some geometric properties of the complex-valued kernel \(\alpha \)-harmonic mappings, such as area, fully starlikeness and fully convexity of order \(\gamma \), \(\gamma \in [0,1)\), are explored. Furthermore, for a class of given boundary function, the Radó–Kneser–Choquet-type

This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor \(\mathcal {D}(u)\) to the 3D Navier–Stokes equations in Lorentz spaces. It is shown that a Leray–Hopf weak solution is regular on (0, T] provided that the norm \(\Vert \lambda _{2}^{+}\Vert _{L^{p,\infty }(0,T; L ^{q,\infty }(\mathbb {R}^{3}))} \) with \( {2}/{p}+{3}/{q}=2\) \((

We provide sufficient conditions for the existence of one positive solution for a fourth--order beam equation with a discontinuous nonlinear term. Also a multiplicity result is established. They are based on a recent generalization of the Krasnosel’skiĭ fixed point theorem in cones.

Most important examples of null hypersurfaces in a Lorentzian manifold admit an integrable screen distribution, which determines a spacelike foliation of the null hypersurface. In this paper, we obtain conditions for a codimension two spacelike submanifold contained in a null hypersurface to be a leaf of the (integrable) screen distribution. For this, we use the rigging technique to endow the null

In this paper, we provide some exact formulas for the projective dimension and regularity of powers of edge ideals of some vertex-weighted rooted forests. These formulas are functions of the weight of vertices and the number of edges.

Let \(({\mathcal {C}},{\mathbb {E}},{\mathfrak {s}})\) be an extriangulated category with a proper class \(\xi \) of \({\mathbb {E}}\)-triangles. In a previous work, we introduced and studied the \(\xi \)-\({\mathcal {G}}\)projective and the \(\xi \)-\({\mathcal {G}}\)injective dimension for any object in \({\mathcal {C}}\). In this paper, we first give some characterizations of \(\xi \)-\({\mathcal

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by reducing them to different but isomorphic interpretations of an abstract notion, viz. the universal property, which is based on a pair of axioms.

For solving large sparse linear complementarity problems effectively, by utilizing the parametric method, the acceleration strategy and the relaxation technique to the modulus-based matrix splitting (MMS) iteration method, we develop the accelerated relaxation MMS (ARMMS) iteration method, which generalizes the generalized accelerated MMS (GAMMS) and the relaxation MMS (RMMS) ones proposed recently

Phase transitions in a model of van der Waals fluid flows in a nozzle with discontinuous cross-sectional area are investigated. The model admits a physically unstable elliptic region which causes phase transitions, and a jump in cross-sectional area which causes stationary contact waves. Compositions between waves in different characteristic fields are constructed differently in subsonic or supersonic

In this article, we study the following Kirchhoff–Schrödinger–Poisson system with pure power nonlinearity $$\begin{aligned} \left\{ \begin{array}{ll} -\Bigl (a+b \displaystyle \int _{\mathbb {R}^3}|\nabla u|^2{\text {d}}x\Bigr )\Delta u+V(x) u+K(x) \phi u= h(x)|u|^{p-1}u, &{}x\in \mathbb {R}^3, \\ -\Delta \phi =K(x)u^2, &{}x\in \mathbb {R}^3, \end{array} \right. \end{aligned}$$ where a, b are positive

In this paper, we prove an n-dimensional radially flat gradient shrinking Ricci solitons with \(div^2W(\nabla f,\nabla f)=0\) is rigid. Moreover, we show that a four-dimensional radially flat gradient shrinking Ricci soliton with \(\text {div}^2W^\pm (\nabla f,\nabla f)=0\) is either Einstein or a finite quotient of \({\mathbb {R}}^4\), \({\mathbb {S}}^2\times {\mathbb {R}}^2\) or \({\mathbb {S}}^3\times

Chen et al. (Appl Math Lett 17:281–285, 2004) conjectured that for even m, \(R(T_n,W_m)=2n-1\) if the maximum degree \(\varDelta (T_n)\) is small. However, they did not state how small it is. Related to this conjecture, it is also interesting to know which tree \(T_n\) causes the Ramsey number \(R(T_n,W_m)\) to be greater than \(2n-1\) whenever m is even. In this paper, we determine the Ramsey number

Under a previously studied condition on the argument of the Selberg zeta function on the critical line, we reach the critical exponent \(\frac{1}{2}\) in the error term of the prime geodesic theorem for the modular group PSL(2,\( \mathbb {Z}\)) outside a set of finite logarithmic measure. We also prove a conditional prime geodesic theorem of Hejhal’s type in this setting without the latter exclusion

A set of vertices W of a graph G is a resolving set if every vertex of G is uniquely determined by its vector of distances to W. In this paper, the Maker–Breaker resolving game is introduced. The game is played on a graph G by Resolver and Spoiler who alternately select a vertex of G not yet chosen. Resolver wins if at some point the vertices chosen by him form a resolving set of G, whereas Spoiler

In this paper, we prove the global well-posedness of the 3-D generalized incompressible Navier–Stokes equations in critical Besov spaces under a polynomial smallness assumption on the initial data. Moreover, we construct a class of initial data with large vertical component, which satisfies that polynomial condition but cannot satisfy the exponential condition in Liu (2020).

The Balaban index and sum-Balaban index of a connected (molecular) graph G are defined as $$\begin{aligned} J(G)&=\frac{m}{\mu +1} \sum _{uv\in E(G)}\frac{1}{\sqrt{\sigma _{G}(u)\sigma _{G}(v)}}~ \text{ and }\\ SJ(G)&=\frac{m}{\mu +1} \sum _{uv\in E(G)}\frac{1}{\sqrt{\sigma _{G}(u)+\sigma _{G}(v)}}, \end{aligned}$$ respectively, where m is the number of edges, \(\mu \) is the cyclomatic number, \(\sigma

This paper concerns with the geometric study of fixed points of a self-mapping on a metric space. We establish new generalized contractive conditions which ensure that a self-mapping has a fixed disc or a fixed circle. We introduce the notion of a best proximity circle and explore some proximal contractions for a non-self-mapping as an application. Necessary illustrative examples are presented to highlight

In this paper, we consider simple connected weighted graphs in which the edge weights are positive numbers. We obtain several upper bounds on the spectral radius and the signless Laplacian spectral radius of irregular weighted graphs, which extend some known results for irregular unweighted graphs.

We study the existence of radial solutions for the p-Laplacian Neumann problem with gradient term of the type $$\begin{aligned} \left\{ \begin{array}{l} -\Delta _{p}u=f(|x|,u,x\cdot \nabla u)\quad \text {in} ~\varOmega ,\\ \displaystyle \frac{\partial u}{\partial \mathbf{n} }=0\quad \text {on}~ \partial \varOmega , \end{array} \right. \end{aligned}$$ where \(\Delta _pu=\text {div}(|\nabla u|^{p-2}\nabla