In this article, we discuss, by Nevanlinna theory, the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions. We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem. These results extend the existing achievements of some scholars.

In this paper, we study the generalized lower order of entire functions defined by Dirichlet series. By constructing the Newton polygon based on Knopp-Kojima’s formula, we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.

We consider the Schrödinger-Poisson system with nonlinear term Q(x)|u|p−1u, where the value of \(\mathop {\lim}\limits_{\left| x \right| \to \infty} \,\,Q\left(x \right)\)Q(x) may not exist and Q may change sign. This means that the problem may have no limit problem. The existence of nonnegative ground state solutions is established. Our method relies upon the variational method and some analysis tricks

In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions (n ≥ 4). We use the Green’s function method. Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system. We show that the decay rates of the solution for the same problem are different in even dimensions and odd dimensions. It is shown

This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class \({\mathbb F}\) which contains Dirichlet ℒ-functions, ℒ-functions in the extended Selberg class, or some periodic functions. We prove that the Euler Γ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are

We discuss the set-valued dynamics related to the theory of functional equations. We look for selections of convex set-valued functions satisfying set-valued Euler-Lagrange inclusions. We improve and extend upon some of the results in [13, 20], but under weaker assumptions. Some applications of our results are also provided.

In this paper, we give a simpler proof for Ohta’s theorems [1995, Ann. Inst. Henri Poincare, 63, 111; 1995, Diff. Integral Eq., 8, 1775] on the strong instability of the ground states for a generalized Davey-Stewartson system. In addition, a sufficient condition is given to ensure the nonexistence of a minimizer for a variational problem, which is related to the stability of the standing waves of the

In this article, we study the blow-up solutions for a case of b-family equations. Using the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtain five types of blow-up solutions: the hyperbolic blow-up solution, the fractional blow-up solution, the trigonometric blow-up solution, the first elliptic blow-up solution, and the second elliptic blow-up solution

Multi-parameter mixed Hardy space \(H_{{\rm{mix}}}^p\) is introduced by a new discrete Calderón’s identity. As an application, we obtain the \(H_{{\rm{mix}}}^p \to {L^p}\left({{ℝ^{{n_1} + {n_2}}}} \right)\) boundedness of operators in the mixed Journé’s class.

We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space. The underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous. A weak convergence result is obtained under reasonable assumptions on the variable step-sizes. We also give the strong convergence result for when the underline

In this paper we consider one dimensional mean-field backward stochastic differential equations (BSDEs) under weak assumptions on the coefficient. Unlike [3], the generator of our mean-field BSDEs depends not only on the solution (Y, Z) but also on the law PY of Y. The first part of the paper is devoted to the existence and uniqueness of solutions in Lp, 1 < p ≤ 2, where the monotonicity conditions

In this paper, we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit. As an application, we obtain the convergence of random attractors for non-autonomous stochastic reaction-diffusion equations on unbounded domains, when the density of stochastic noises approaches zero. The weak convergence of solutions is proved by

We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.

This paper is concerned with the large-time behavior of solutions to the Cauchy problem of a one-dimensional viscous radiative and reactive gas. Based on the elaborate energy estimates, we develop a new approach to derive the upper bound of the absolute temperature by avoiding the use of auxiliary functions Z(t) and W(t) introduced by Liao and Zhao [J. Differential Equations, 2018, 265(5): 2076–2120]

In this article, we investigate a stochastic Galerkin method for the Maxwell equations with random inputs. The generalized Polynomial Chaos (gPC) expansion technique is used to obtain a deterministic system of the gPC expansion coefficients. The regularity of the solution with respect to the random is analyzed. On the basis of the regularity results, the optimal convergence rate of the stochastic Galerkin

We establish uniqueness theorems of L-functions in the extended Selberg class, which show how an L-function and a meromorphic function are uniquely determined by their shared values in two finite sets. This can be seen as a new solution of a problem proposed by Gross.

We study the following nonlinear fractional Schrödinger-Poisson system with critical growth: $$\left\{ {\begin{array}{*{20}{c}} {{{( - \Delta )}^s}u + u + \phi u = f(u) + {{\left| u \right|}^{2_s^*}}u,}&{x \in {\mathbb{R}^3},} \\ {{{( - \Delta )}^t}\phi = {u^2},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}&{x \in {\mathbb{R}^3},} \end{array}} \right.$$((0.1)) where 0 < s, t < 1, 2s + 2t>3 and \(2_s^*

In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model. Different from others studies, we consider the physical case that the mobilities of the charges are different. The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.

In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines. In this paper we shall consider the distribution problem of Julia sets of meromorphic maps. We shall show that the Julia set of a transcendental meromorphic map with at most finitely many poles cannot be contained

In this article, we consider to solve the inverse initial value problem for an inhomogeneous space-time fractional diffusion equation. This problem is ill-posed and the quasi-boundary value method is proposed to deal with this inverse problem and obtain the series expression of the regularized solution for the inverse initial value problem. We prove the error estimates between the regularization solution

We show that a flow or a semiflow with a weak form of reparametrized gluing orbit property has positive topological entropy if it is not minimal.

Suppose that A and B are two positive-definite matrices, then, the limit of (Ap/2BpAp/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter formula. In this article, we generalize the usual product of matrices to the Hadamard product denoted as * which is commutative, and obtain the explicit formula of the limit (Ap * Bp)1/p as p tends to 0. Furthermore, the existence of the limit of

In this article, we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions. By constructing some new Lagrange-type identities and two fundamental functions, we obtain not only the existence, the simplicity, and the interlacing properties of the real eigenvalues, but also the oscillation properties, orthogonality of the eigenfunctions

The goal of this article is to study the asymptotic analysis of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. The yield stress and the constant viscosity are assumed to vary with respect to the thin layer parameter ε. Firstly, the problem statement and variational formulation are formulated. We then obtained the existence and the uniqueness result of a weak

In this article, we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel [1]. Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators (when it exists). The last

In this article, we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces \(F_\varphi^2\). Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.

In this article, a new algorithm is presented to solve the nonlinear impulsive dif- ferential equations. In the first time, this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations. Then, the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is

Within the zero curvature formulation, a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type. The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity. When the involved two potential vectors are scalar, all the resulting integrable lattice

This article mainly considers the blow up phenomenon of the solution to the wave-hartree equation utt − Δu = (|x|−4 * |u|2)u in the energy space for high dimensions d ≥ 5. The main result of this article is that: if the initial data (u0, u1) satisfy the conditions E(u0, u1) < E(W, 0) and \(\parallel\triangledown{u_0}\parallel_2^2>\parallel\triangledown{W}\parallel_2^2\) for some ground state W, then

This article is committed to deal with measure of non-compactness of operators in Banach spaces. Firstly, the collection \(\mathcal{C}(X)\) (consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication) is a normed semigroup, and the mapping J from \(\mathcal{C}(X)\) onto \(\mathcal{F}(\Omega)\) is a fully order-preserving positively

This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions $$\begin{cases}u_t=\triangledown\cdot(D(u)\triangledown{u})-\triangledown\cdot(S(u)\triangledown{v})+f(u), & x \in \Omega, t > 0\\v_t=\Delta{v}+w-v, & x \in \Omega, t > 0,\\w_t=u-w, & x \in \Omega, t > 0,\end{cases}$$

In this article, we use the robust optimization approach (also called the worst-case approach) for finding e-efficient solutions of the robust multiobjective optimization problem defined as a robust (worst-case) counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions. Namely, we establish both necessary and sufficient

In this work, we apply the Brzdęk and Ciepliński’s fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form $$f(ax+by)=af(x)+bf(y),$$ where a, b ∈ ℕ and f is a mapping from a commutative group (G, +) to a 2-Banach space (Y, ∥ ·, · ∥). Our results are generalizations of main results of Brzdęk and Ciepliński [J Brzdęk, K Ciepliński. On a fixed

Let B = {BH(t)}t≥0 be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Consider the functionals of k independent d-dimensional fractional Brownian motions $$\frac{1}{\sqrt{n}}\int_{0}^{e^{{nt}_1}} \cdot\cdot\cdot\int_{0}^{e^{{nt}_k}} f(B^{H,1}(s_1)+\cdot\cdot\cdot+B^{H,k}(s_k)){\rm{d}}s_1\cdot\cdot\cdot{{\rm{d}}s_k},$$ where the Hurst index H = k/d. Using the method of moments

In this article, we study the following critical problem involving the fractional Laplacian: $$\begin{cases}(-\Delta)^{\frac{\alpha}{2}}u-\gamma\frac{u}{|x|^\alpha}=\lambda\frac{|u|^{q-2}}{|x|^s}+\frac{u^{2_\alpha^*(t)-2}u}{|x|^t} & in\;\Omega, \\u=0 & in\;\mathbb{R}^N\backslash\Omega,\end{cases}$$ where Ω ⊂ ℝN (N > α) is a bounded smooth domain containing the origin, α ∈ (0,2), 0 ≤ s, t < α, 1 ≤ q

In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity, the second spacial derivative of the square root of the density, and the first order time derivative and first order spacial derivative of the square root

This article discusses the synchronization problem of singular neutral complex dynamical networks (SNCDN) with distributed delay and Markovian jump parameters via pinning control. Pinning control strategies are designed to make the singular neutral complex networks synchronized. Some delay-dependent synchronization criteria are derived in the form of linear matrix inequalities based on a modified Lyapunov-Krasovskii

For a given T > 0, we prove, under the global ARS-condition and using the Nehari manifold method, the existence of a T-periodic solution having the W-symmetry introduced in [21], for the hamiltonian system $$\ddot{z}+V^\prime(z)=0,\;\;\;z\in\mathbb{R}^N\;\;\;N\in\mathbb{N}*.$$ Moreover, such a solution is shown to have T as a minimal period without relaying to any index theory. A multiplicity result

In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the \(\mathcal{A}\)-harmonic approximation technique. In this article, we extend the result of Shuhong Chen and Zhong Tan [7] and Giaquinta and Modica [18] to the stationary Navier-Stokes system

In this article, we consider a fully nonlinear partial differential equation which can be expressed as a sum of two Monge-Ampère operators acting in different two-dimensional coordinate sections. This equation is elliptic, for example, in the class of convex functions. We show that the notion of Monge-Ampère measures and Aleksandrov generalized solutions extends to this equation, subject to a weaker

Smillie and Weiss proved that the set of the areas of the minimal triangles of Veech surfaces with area 1 can be arranged as a strictly decreasing sequence {an}. And each an in the sequence corresponds to finitely many affine equivalent classes of Veech surfaces with area 1. In this article, we give an algorithm for calculating the area of the minimal triangles in a Veech surface and prove that the

In higher dimension, there are many interesting and challenging problems about the dynamics of non-autonomous Chafee-Infante equation. This article is concerned with the asymptotic behavior of solutions for the non-autonomous Chafee-Infante equation \(\frac{\partial u}{\partial t}-\Delta u = \lambda(t)(u-u^3)\) in higher dimension, where λ(t) ∈ C1 [0, T] and λ(t) is a positive, periodic function. We

This article proposes the maximum test for a sequence of quadratic form statistics about score test in logistic regression model which can be applied to genetic and medicine fields. Theoretical properties about the maximum test are derived. Extensive simulation studies are conducted to testify powers robustness of the maximum test compared to other two existed test. We also apply the maximum test to

The asymptotic normality of the fixed number of the maximum likelihood estimators (MLEs) in the directed finite weighted network models with an increasing bi-degree sequence has been established recently. In this article, we further derive the central limit theorem for linear combinations of all the MLEs with an increasing dimension when the edges take finite discrete weight. Simulation studies are

Let (B, ∥ · ∥) be a Banach space, (Ω, F, P) a probability space, and L0 (F, B) the set of equivalence classes of strong random elements (or strongly measurable functions) from (Ω, F, P) to (B, ∥ · ∥). It is well known that L0 (F, B) becomes a complete random normed module, which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function

The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer order ώ ∈ (1, 2]. The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder’s fixed point theorem for existence. Also, we establish some conditions under which the solution of the considered

This article is concerned with the 3D nonhomogeneous incompressible magneto- hydrodynamics equations with a slip boundary conditions in bounded domain. We obtain weighted estimates of the velocity and magnetic field, and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states.

In this article, we consider the following coupled fractional nonlinear Schrödinger system in ℝN$$\begin{cases}(-\Delta)^s u+P(x)u=\mu _1 |u|^{2p-2}u+\beta|v|^p|u|^{p-2}u, & x \in \mathbb{R}^N, \\ (-\Delta)^s v+Q(x)v=\mu_2|v|^{2p-2}v+\beta|u|^p|v|^{p-2}v, & x \in \mathbb{R}^N, \\ u, v \in H^s(\mathbb{R}^N), \end{cases}$$ where \(N \ge 2,0 < s < 1,1 < p < \frac{N}{{N - 2s}},{\mu _1} > 0,\mu _{2} > 0\)

We study the strong instability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction under the mass resonance condition in dimension d = 5.

The unified Ω-series of the Gauss and Bailey \(_2F_1(\frac{1}{2})\)-sums will be investigated by utilizing asymptotic methods and the modified Abel lemma on summation by parts. Several remarkable transformation theorems for the Ω-series will be proved whose particular cases turn out to be strange evaluations of nonterminating hypergeometric series and infinite series identities of Ramanujan-type, including

With the aid of Nevanlinna value distribution theory, differential equation theory and difference equation theory, we estimate the non-integrated counting function of meromor- phic solutions on composite functional-differential equations under proper conditions.We also get the form of meromorphic solutions on a type of system of composite functional equations. Examples are constructed to show that

We obtain characterizations of nearly strong convexity and nearly very convexity by using the dual concept of S and WS points, related to the so-called Rolewicz’s property (α). We give a characterization of those points in terms of continuity properties of the identity mapping. The connection between these two geometric properties is established, and finally an application to approximative compactness

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets. For the three-dimensional steady non-isentropic compressible Euler system with frictions, we constructe a family of transonic shock solutions in rectilinear ducts with square cross-sections. In this article, we are devoted to proving rigorously that a large class of these transonic shock solutions are stable, under

In this article, we study the approximate controllability results for an integroquasilinear evolution equation with random impulsive moments under sufficient conditions. The results are obtained by the theory of C0 semigroup of bounded linear operators on evolution equations and using trajectory reachable sets. Finally, we generalize the results too with and without fixed type impulsive moments.

This article studies the initial-boundary value problem for a three dimensional magnetic-curvature-driven Rayleigh-Taylor model. We first obtain the global existence of weak solutions for the full model equation by employing the Galerkin’s approximation method. Secondly, for a slightly simplified model, we show the existence and uniqueness of global strong solutions via the Banach’s fixed point theorem

In this article, by employing an oscillatory condition on the nonlinear term, a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence

In this article, we study the existence and asymptotic behavior of multi-bump solutions for nonlinear Choquard equation with a general nonlinearity $$-\Delta u + (\lambda a(x) + 1)u = \left(\frac{1}{|x|^\alpha}* F(u)\right) f(u) \; in \; \mathbb{R}^N,$$ where N ≥ 3, 0 < α < min{N, 4}, λ is a positive parameter and the nonnegative potential function a(x) is continuous. Using variational methods, we

In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are two attractive features of the methods shown in this article: 1) a partition of unity is used to generate a series of local and independent subproblems to guarantee

In this paper, we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds. Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds.