In this paper, we study the multiplicity of solutions for a class of p-Laplacian type fractional differential equations with both instantaneous and non-instantaneous impulses. By using the critical points theorem of B. Ricceri, a theorem is developed for the existence of at least three solutions for the impulsive problem depending on two parameters.

In this paper, a super extension of Sawada–Kotera hierarchy is proposed. This hierarchy is derived by considering a third order Lax operator with a quasi-local term. Bi-Hamiltonian structure is constructed for the super Sawada–Kotera hierarchy.

We consider the following problem with the critical exponent p−1=r ut=d1Δu−a1u+upvq+δ1(x,t),x∈Ω,t>0,vt=d2Δv−a2v+urvs+δ2(x,t),x∈Ω,t>0,∂u∂η=∂v∂η=0,x∈∂Ω,t>0,u(x,0)=u0(x),v(x,0)=v0(x),x∈Ω.Here q,r,d1,d2,a1 and a2 are positive constants, p>1, s>−1, δ1, δ2, u0 and v0 are nonnegative smooth functions, Ω⊂Rd(d≥1) is a bounded smooth domain. Whether d1≠d2 or d1=d2, we establish the results on the finite-time

We study the existence of forced traveling waves and gap formations for the lattice Lotka–Volterra competition system in a shifting habitat. By virtue of upper-lower solution method, we establish that the system admits a forced wave provided that the shifting speed of climate change falls in a certain interval. When the shifting speed is outside the range (except for the two endpoints), gap formations

Existence of global classical solutions with a certain periodic asymptotic behavior of a class of reaction diffusion systems with chemotactic terms is demonstrated. This class contains a system consisting of a parabolic equation with a logistic-like term describing the behavior of a biological species and an ordinary differential equation modeling the concentration of a chemical substance throughout

In this letter, a fractional-order prey-predator model with Holling III type functional response and discontinuous harvest is considered. The non-negative and boundedness of the model are proved. In addition, some conditions for the existence and stability of the positive equilibrium point are proposed. Finally, numerical simulations are given to confirm the correctness of theorem.

In this paper, based on the special property of the lowest order rectangular Raviart–Thomas element on the rectangulation and skillfully dealing with the nonlinear term, the superclose estimates for original and flux variables in L∞(L2)-norm are derived firstly for the semilinear parabolic equation with backward Euler discretization in temporal direction. Then, by using a simple and efficient interpolation

This paper is devoted to study the existence of nontrivial solutions to a fractional Kirchhoff type problem with the nonlinearity term having critical exponential growth, which is related to the fractional Trudinger–Moser type inequality.

This paper is concerned with a fractional order SEIR model with general incidence rate. Local and uniform asymptotic stability of equilibria is established for this model. Our results cover and improve some known results.

This paper is devoted to the problem of solving fractional nabla difference equations. We obtain a general expression of the solution of the fractional nabla difference equation which is different from the discrete Mittag-Leffler function. As an application, we obtain a new asymptotic result expressed in terms of the coefficients and fractional order. Our result is not covered by previously known results

With the aid of the direct bilinear method, the formula of N-soliton solution to the generalized (3 + 1)-dimensional Yu–Toda–Sasa–Fukuyama (gYTSF) equation is succinctly obtained. By means of long-wave limit method on 2M-soliton solutions under special parameter constraints, M-order lumps can be successfully constructed. Furthermore, the propagation orbit, velocity and extremum of the 1-order lump

This paper describes a new algorithm for computing Nonnegative Low Rank Matrix (NLRM) approximation for nonnegative matrices. Our approach is completely different from classical nonnegative matrix factorization (NMF) which has been studied for more than twenty five years. For a given nonnegative matrix, the usual NMF approach is to determine two nonnegative low rank matrices such that the distance

A general variable coefficient (gVC) Burgers equation with linear damping term has been investigated by using simplified homogeneous balance (SHB) method. The generalized Cole–Hopf transformation for the gVC Burgers equation with linear damping term has been derived out if the damping coefficient satisfies a certain constraint condition. By means of the generalized Cole–Hopf transformation, the exact

In this article we present a generalization of the WENO algorithm of order six for data discretized in the point values introduced in Amat et al. (2019). This generalization requires a slight modification of the mentioned algorithm. The objective is to obtain a new WENO algorithm of order 2r that is capable of rising the accuracy of the interpolation step by step close to the discontinuities. In order

After some remarks on a possible zero-curvature formulation we establish local well-posedness for the double extended cubic peakon system.

We propose a new finite element approach, which is different than the classic Babuška–Osborn theory, to approximate Dirichlet eigenvalues. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for conforming finite elements is proved using the abstract approximation theory for holomorphic operator functions. The spectral indicator

We study the motion of a hypersurface in a cylinder driven by its (generalized) Gauss curvature. Some special cases of the problem can be used to model the abrasion of a stick on its ends. First we consider the case where the slope of the hypersurface on the cylinder boundary is a positive constant h, and seek for a radially symmetric translating solution. Then we consider the case where the boundary

In this article, we investigate a class of stochastic fractional differential equations (SFDEs) with time-delays. Under some novel assumptions, we obtain an averaging principle for the solution of the considered system. Finally, an example with numerical simulation is given to show the theoretical result.

Under investigation in this manuscript is the coupled Hirota equations, which describe the propagation of ultrashort optical pulses in a birefringent fiber or collision of the two waves arisen by severe weather in deep ocean. Based on the generalized Darboux transformation derived before, we obtain the semirational solutions, and properties of the solitons are discussed in detail: Elastic collisions

In this paper, we will focus on the (2+1)-dimensional complex modified Korteweg–de Vries and Maxwell–Bloch (cmKdVMB) system. According to the correlative Lax pair, the N-fold generalized Darboux Transformations (DT) will be constructed. By virtue of the DT obtained, some rogue wave solutions will be derived from the nonvanishing continuous wave (cw) backgrounds. Meanwhile, the dynamic features of those

The paper discusses the problem of necessary and sufficient stability conditions for a test fractional delay differential equation and its discretization. First, we recall the existing condition for asymptotic stability of the exact equation and consider an appropriate fractional delay difference equation as its discrete counterpart. Then, using the Laplace transform method combined with the boundary

In this work, we are concerned with the lattice Boltzmann method for anisotropic convection–diffusion equations (CDEs). We prove that the collision matrices of many widely used lattice Boltzmann models for such equations admit an elegant property, which guarantees the second-order accuracy of the half-way anti-bounce-back scheme. Numerical experiments validated our results for both two- and three-dimensional

For the first time, a general integration scheme is proposed which can be employed in the development of quadrature elements with nodes of any type. With the proposed scheme, explicit formulations of quadrature elements with an arbitrary number of nodes can be derived indirectly via the differential quadrature law. Similar to the conventional finite element method, either reduced or full integration

Considered herein is the Cauchy problem of a modified two-component Dullin–Gottwald–Holm system. We derive a new sufficient condition on the initial data to guarantee that the corresponding solution to this system blows up in finite time.

The aim of this paper is to study the symmetry of the positive solutions of the nonlocal critical system of Hartree type: −Δu=∫RNv2μ⋆(y)|x−y|μdyv2μ⋆−1−Δv=∫RNu2μ⋆(y)|x−y|μdyu2μ⋆−1 where 0<μ

Linear higher-order delayed systems of discrete equations Δ2x(k)+Ax(k−m)=f(k),k=0,1,…are considered where m is a positive integer, x:{−m,−m+1,…}→Rn, Δ2 is the second-order forward difference, A is an n×n constant real matrix and f:{0,1,…}→Rn. Representations of solutions are derived by means of new types of matrix functions of delayed type. Advantages over previous results are discussed with open problems

In this paper, we study the nonexistence of solutions for the quasilinear elliptic equations (1)±(Δpu+νΔp(u2)u)=h(x)um+H(x)un,x∈RNand (2)±(Δpu+νΔp(u2)u)=g(x,u)+H(x)eu,x∈RN,where N≥3,ν≥0,m≤p−11 and h(x),H(x)>0, g(x,u)≥0 in RN×[0,∞). We establish conditions sufficient to ensure the nonexistence of bounded positive solutions for (1) and (2).

In this paper we investigate the existence, asymptotic behavior and uniform p-integrability of fractional resolvent families generated by sectorial operators in Banach spaces. As a consequence, we obtain properties on the behavior of mild solutions to abstract fractional Cauchy problems for the Caputo and Riemann–Liouville fractional derivatives.

In this paper double Wronskian solutions to the Broer–Kaup–Kupershmidt (BKK) equation are investigated by using of Hirota method and binary bell polynomials. By introducing different auxiliary functions, the bilinear equations for the BKK equation in different forms are obtained respectively. Based on the distinct Hirota bilinear equations, two groups of double Wronskian solutions to the BKK equation

In this paper, a novel local knot method (LKM) is presented to solve the 2D and 3D convection–diffusion–reaction equations in arbitrary domains. Contrary to the traditional boundary knot method, the proposed scheme requires the nodes not only on the boundary but also inside the domain. For each node, we can find a local subdomain containing a certain number of neighboring nodes. Utilizing the non-singular

The consistent Riccati expansion (CRE) is used to the Drinfel’d–Sokolov–Wilson (DSW) equation. It demonstrates that the DSW equation is the CRE solvability system. The bilinear form of the DSW equation is constructed by the truncated Painlevé method. One rogue wave including the dark and bright types is explicitly found via choosing a quadratic function in the bilinear form of the DSW equation. The

In this letter, we derive the isospectral and nonisospectral soliton hierarchies of a higher-order Zakharov–Shabat spectral problem where nonlinear Schrödinger equation and modified KdV equation are included. Furthermore, it is discussed that the new integrable properties are found about the higher-order Zakharov–Shabat hierarchy, including the master symmetry and the time dependent symmetry.

In this paper, we classify irreducible Darboux polynomials and rational first integrals of the nonstretching Rolie–Poly model by a new method based on the classical characteristic curves method. The classical method has been successfully applied to many systems, but it is not suitable for the nonstretching Rolie–Poly model. We take it as an auxiliary tool to give a preliminary understanding of the

The interface flux plays an important role in designing numerical methods for scalar conservation laws with discontinuous flux function in space. Based on the (A,B)-type entropy solutions defined by Bürger et al. (2009), we introduce a new modified Local Lax–Friedrichs interface flux to approximate this system. The interface flux is Lipschitz continuous and monotone with respect to its two variables

By introducing multiple pairs of different time-varying delays in the time-dependent birth functions, this paper proposes explores a patch structure Nicholson’s blowflies system involving distinctive delays. Without assuming the uniform positiveness of the dead rate and the boundedness of coefficients, the global stability of the considered system is established by employing some novel inequality techniques

This paper is concerned with a blow-up criterion of strong solutions for the chemotaxis-fluid equations in three-dimensional whole space. The so-called Cole-Hopf type transformation is used to remove the singularity at c=0 caused by the chemotactic sensitivity function. Then, the Serrin’s type blow-up criterion is obtained for the existence of strong solutions to the transformed system.

Variational–hemivariational inequalities and hemivariational inequalities form a powerful mathematical tool in modeling and studying problems in science and engineering where non-smooth, non-monotone and multi-valued relations among different physical quantities are present. In this paper, we consider the numerical solution of optimal control problems for variational–hemivariational inequalities or

In the paper, we study a class of biharmonic equations with singular weight functions as follows: Δ2u−βΔpu+Vλ(x)u=fxuq−2uinRN,u∈H2(RN),where N≥3,Δ2u=Δ(Δu), Δpu=div(|∇u|p−2∇u),β≥0 is a parameter, 20. Under some suitable assumptions on a,b and f, we obtain the existence and multiplicity of nontrivial solutions for λ large enough. An interesting phenomenon is that

This paper is concerned with a numerical method for the time-fractional Benjamin–Bona–Mahony (BBM) equation whose solution typically exhibits a weak singularity at the initial time. Lyu and Vong (2019) presented a linearized difference method of second-order in space and third-order in time. We improve their result by proposing a linearized and compact difference method which is fourth-order in space

In this note we investigate Liouville theorem of plane shear thickening fluids in the whole space R2. By applying a different approach of Point-wise Behavior Theorem, we improve the known Liouville type results by Fuchs (2012) and Zhang (2015).

This paper focuses on the stability problem of linear time-delay systems. Firstly, a generalized vectors-based multiple integral inequality (GVMII) is presented, which can treat some existing results as its special cases. Secondly, based on the multiple integral inequality, a new delay-dependent stability criterion is derived for time-delay systems. Finally, a numerical example is given to illustrate

The boundary knot method (BKM) is applied to the Helmholtz equation in 2D bounded simply-connected domains, to show high accuracy of the solutions obtained by not many fundamental solutions (FS) used. When the Bessel function is chosen as the FS, the optimal polynomial convergence rates are obtained for disk domains. Moreover, the bounds of condition number (Cond) are derived for disk domains, to show

We study the reaction–diffusion Lotka–Volterra predator–prey model with Dirichlet boundary condition. In the case of equal diffusion rates and equal growth rates, the synchronized steady state solution is proved to be locally asymptotically stable.

Based on the conformable derivative approach, conformable advection–diffusion equations with equilibrium and non-equilibrium adsorption for contaminant migration in porous media are proposed, and the analytical solutions are obtained via the Laplace transform method in this work. In addition, concentration profiles are carried out for the illustrative explanations of the analytical solutions. This

Given multiple univariate or multivariate real polynomials f1,…,fm and a desired real zero z, this paper studies the problem of calculating a real polynomial f˜ such that f˜(z)=0 and the distance between f˜ and f1,…,fm is minimal, where the distance is defined by a norm pair (ℓr,ℓs). Though geometrical and numerical algorithms have been studied in previous works, only few norm pairs can be dealt with

A coherently coupled nonlinear Schrödinger system with the positive coherent coupling is studied in this paper, and high-order semi-rational solutions are derived by the generalized Darboux transformation. Dynamic of the second-order semi-rational solutions is found to be of three types: collisions between the one-hump soliton and breather (double-hump rogue waves), collisions between the double-hump

This paper deals with the following Kirchhoff type problem (0.1)−a+b∫RN|∇u|2Δu=λK(x)uq−1+u2∗−1,u>0,x∈RN,where N≥3, K∈L1(RN)∩L∞(RN), constants a,b>0, the parameter λ>0 and 2≤q<2∗≔2N∕(N−2). Using the finite-dimensional reduction approach, we prove that problem (0.1) admits at least a positive solution.

In this study, we develop a second-order finite difference scheme based on the shifted convolution quadrature (SCQ) framework that approximates the space-fractional derivatives at a shifted node xn−θ where θ may not necessarily be an integer. By applying the proposed method for a space-fractional advection-diffusion equation in the spacial direction and the Crank–Nicolson scheme for the time variable

This paper, focusing on the fractional neutral stochastic differential equations (FNSDEs) in the Euclidean space Rn, successfully provides the first evidence of a new fractional averaging theorem via rigorous mathematical deductions. With the help of integration by part, the fractional term is handled simply and ingeniously. Based on this new idea, we show that the mild solutions of two fractional

Nonlocal residual symmetries are constructed for the generalized dispersive water waves (GDWW) system. The linear superposed multiple residual symmetries are presented and localized, which give rise to nth Bäcklund transformation in terms of determinant. Based on the direct connection between the truncated Painlevé expansion and the consistent tanh expansion (CTE) method, we derive exact interaction

Richtmyer–Meshkov instability (RMI) plays an important role in nature and technology, including supernovae, fusion, scramjets and nano-fabrication. Canonical RMI is induced by a steady shock and impulsive acceleration. In realistic environments the acceleration is often variable. We focus on the accelerations with power-law time-dependence, identify the values of the power-law exponent for which the

This paper is a continuous work of Liu et al. (2017, first order) and Xu et al. (2019, second order) for affine-periodic solutions to ordinary differential equations. It is a hard problem to obtain satisfied extremum principles. In this paper, we give several extremum principles (Theorem 2.1 and Lemma 2.2) for affine-periodic problems, especially for the case of higher order systems. By these extremum

We consider ground states of the drifting Schrodinger equation iut−Δu+∇h⋅∇u=λV|u|p−1u (where p>1+2N and (N−2)p

We are interested in multiple solutions for a class of Schrödinger-Maxwell system. Using variational methods and analytic tricks, we obtain infinitely many high energy solutions under some mild assumptions. Our results generalize and improve some recent results.

Kawasaki disease, also referred to as mucocutaneous lymph node syndrome (MCLS), is an autoimmune disease. In this paper, we consider an ordinary differential equation model of Kawasaki disease pathogenesis. In this model, there exhibits forward∕backward bifurcation. By constructing suitable Lyapunov functions and using Lyapunov-LaSalle invariance principle, we establish some practical sufficient conditions

We prove uniqueness of positive solutions for the problem −Δpu=λf(u)uαinΩ,u=0 on∂Ω,where p>1+α,α∈(0,1),Ω is bounded domain in Rn with smooth boundary ∂Ω, f:[0,∞)→(0,∞) is nondecreasing with f(z)∕zα decreasing for z large, and λ is a large parameter.

By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ, our criteria improve a number of related results reported in the literature.

A scheme is proposed to generate stable spatiotemporal solitons (STs) in a cold Rydberg atomic system with a Bessel Lattice (BL) potential, by utilizing electromagnetically induced transparency (EIT). We investigate the existence and stability of these three-dimensional (3D) STs supported by BL in nonlocal nonlinear media. The results show that the system can support slow STs with low light intensity

Randomized longitudinal clinical trials are the gold standard to evaluate the effectiveness of interventions among different patient treatment groups. However, analysis of such clinical trials becomes difficult in the presence of missing data, especially in the case where the study endpoints become difficult to measure because of subject dropout rates or/and the time to discontinue the assigned interventions

The nucleated polymerization model is a mathematical framework that has been applied to aggregation and fragmentation processes in both the discrete and continuous setting. In particular, this model has been the canonical framework for analyzing the dynamics of protein aggregates arising in prion and amyloid diseases such as as Alzheimer's and Parkinson's disease. We present an explicit steady-state