Articles

Non-real eigenvalues of nonlocal indefinite Sturm–Liouville problems

The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite Sturm–Liouville differential equation with nonloca...

Authors: Fu Sun, Kun Li, Jiangang Qi and Baochao Liao

Sign-constancy of Green’s functions for impulsive nonlocal boundary value problems

Authors: A. Domoshnitsky and Iu. Mizgireva

Blow-up results for a quasilinear von Karman equation of memory type

In this paper, we consider the blow-up result of solution for a quasilinear von Karman equation of memory type with nonpositive initial energy as well as positive initial energy. For nonincreasing function

Authors: Mi Jin Lee and Jum-Ran Kang

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Authors: Shiqi Ma and Xuemei Zhang

On a weak solution matching up with the double degenerate parabolic equation

Authors: Sujun Weng

Existence of solutions for a nonhomogeneous Dirichlet problem involving \(p(x)\)-Laplacian operator and indefinite weight

Authors: Aboubacar Marcos and Aboubacar Abdou

Uniqueness result for a fractional diffusion coefficient identification problem

In this paper, we establish an identifiability result for the coefficient identification problem in a fractional diffusion equation in a bounded domain from the observation of the Cauchy data on particular sub...

Authors: Fadhel Jday and Ridha Mdimagh

Existence of multiple positive solutions for nonhomogeneous fractional Laplace problems with critical growth

We prove the existence of multiple positive solutions of fractional Laplace problems with critical growth by using the method of monotonic iteration and variational methods.

Authors: Fang Wang and Yajing Zhang

A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

A multiple integral finite volume method combined and Lagrange interpolation are applied in this paper to the Rosenau-RLW (RRLW) equation. We construct a two-level implicit fully discrete scheme for the RRLW e...

Authors: Cui Guo, Fang Li, Wenping Zhang and Yuesheng Luo

Shape optimization of turbine blade cooling system using topological sensitivity analysis method

The topological sensitivity analysis method gives the variation of a criterion with respect to the creation of a small hole in the domain. In this paper, we use this method to solve an inverse problem related ...

Authors: Emna Ghezaiel, Maatoug Hassine, Mohamed Abdelwahed and Nejmeddine Chorfi

Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

Authors: Yan Dong, Guangwei Du and Kelei Zhang

Discontinuous generalized double-almost-periodic functions on almost-complete-closed time scales

In this paper, we introduce the concept of almost-complete-closed time scales (ACCTS) that allows independent variables of functions to possess almost-periodicity under translations. For this new type of time ...

Authors: Chao Wang, Ravi P. Agarwal, Donal O’Regan and Rathinasamy Sakthivel

The critical exponent for fast diffusion equation with nonlocal source

Authors: Chunxiao Yang, Linghua Kong, Yingxue Wu and Qing Tian

The dynamic properties of solutions for a nonlinear shallow water equation

The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation...

Authors: Yeqin Su, Shaoyong Lai and Sen Ming

Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity

This paper is concerned with global existence of large solutions to the initial-boundary value problem of the planar magnetohydrodynamic compressible flow. Under the assumptions that viscosity and heat conduct...

Authors: Wei Li and Zhaoyang Shang

A new application of Schrödinger-type identity to singular boundary value problem for the Schrödinger equation

In this paper, we present a modified Schrödinger-type identity related to the Schrödinger-type boundary value problem with mixed boundary conditions and spatial heterogeneities. This identity can be regarded a...

Authors: Bo Meng

Least energy sign-changing solutions for Kirchhoff–Poisson systems

Authors: Guoqing Chai and Weiming Liu

The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method

This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to t...

Authors: Lizhen Chen, Xiaojing Feng and Xinan Hao

Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity

Authors: Yubo He, Dongdong Qin and Dongdong Chen

Global existence of weak solution for the compressible Navier–Stokes–Poisson system with density-dependent viscosity

In this paper, we are concerned with the existence of global weak solutions to the compressible Navier–Stokes–Poisson equations with the non-flat doping profile when the viscosity coefficients are density-depe...

Authors: Meiying Cui and Wenjing Song

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

In this article, we investigate the effect of surface tension in the Rayleigh–Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linear...

Authors: Xingrui Ma and Xianzhu Xiong

Global existence of solution for multidimensional generalized double dispersion equation

In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in...

Authors: Xiaoqiang Dai

Life span of solutions with large initial data for a semilinear parabolic system coupling exponential reaction terms

In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solu...

Authors: Sen Zhou

Applications of maximum modulus method and Phragmén–Lindelöf method for second-order boundary value problems with respect to the Schrödinger operator

In this paper, we present a reliable combination of the maximum modulus method with respect to the Schrödinger operator (Meng in J. Syst. Sci. Complex. 16:446–452, 2003) and Phragmén–Lindelöf method (Shehu in Mat...

Authors: Zhen Liu

Multiple solutions of fourth-order difference equations with different boundary conditions

In the present paper, a class of fourth-order nonlinear difference equations with Dirichlet boundary conditions or periodic boundary conditions are considered. Based on the invariant sets of descending flow in...

Authors: Yuhua Long, Shaohong Wang and Jiali Chen

Determination of differential pencils with impulse from interior spectral data

Authors: Yongxia Guo, Guangsheng Wei and Ruoxia Yao

Ground state solutions of Nehari–Pohožaev type for a kind of nonlinear problem with general nonlinearity and nonlocal convolution term

Authors: Shuai Yuan and Fangfang Liao

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

We study the nonlinear Rayleigh–Taylor (RT) instability of an inhomogeneous incompressible viscoelastic fluid in a bounded domain. It is well known that there exist strong solutions of RT instability in

Authors: Zhidan Tan and Weiwei Wang

Ground state solutions for fractional Schrödinger equation with variable potential and Berestycki–Lions type nonlinearity

Authors: Jing Chen and Zu Gao

A modified Schrödinger-type identity: uniqueness of solutions for singular boundary value problem for the Schrödinger equation

This paper is devoted to modifying the Schrödinger-type identity related to singular boundary value problem in (Zhang et al. in Bound. Value Probl. 2018:135, 2018). We also present some mathematical consequences ...

Authors: Hongjun He and Zhifeng Pang

Solvability for a class of integral inequalities with maxima on the theory of time scales and their applications

This paper is committed to introducing some Bihari type inequalities for scalar functions of one independent variable under an initial condition associated with an arbitrary time scale ...

Authors: Zareen A. Khan

Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives

By using monotone iterative method, the extremal solutions and the unique solution are obtained for a nonlinear fractional p-Laplacian boundary value problem involving fractional conformable derivatives and nonlo...

Authors: Jianfang Qin, Guotao Wang, Lihong Zhang and Bashir Ahmad

Multiple positive solutions for mixed fractional differential system with p-Laplacian operators

This paper is focused on researching a class of mixed fractional differential system with p-Laplacian operators. Based on the properties of the corresponding Green’s function, different combinations of superlinea...

Authors: Ying Wang

Convergence rates in homogenization of p-Laplace equations

This paper is concerned with homogenization of p-Laplace equations with rapidly oscillating periodic coefficients. The main difficulty of this work is due to the nonlinear structure in this field concerning p-Lap...

Authors: Jie Zhao and Juan Wang

Multiple solutions for quasilinear elliptic problems with concave-convex nonlinearities in Orlicz–Sobolev spaces

Using variational arguments, we establish the existence of two nontrivial solutions for quasilinear elliptic problems in Orlicz–Sobolev spaces, where the nonlinear terms exhibit the combined effects of concave...

Authors: Shujun Wu

Positive solutions of fractional differential equation with two pieces in chain interval and simultaneous Dirichlet boundary conditions

In the current study, by using some fixed point technique such as Banach contraction principle and fixed point theorem of Krasnoselskii, we look into the positive solutions for fractional differential equation

Authors: Vahid Hedayati and Mohammad Esmael Samei

New general decay results in an infinite memory viscoelastic problem with nonlinear damping

Authors: Adel M. Al-Mahdi and Mohammad M. Al-Gharabli

Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems

Authors: Hongxia Shi

Boundedness in a quasilinear chemotaxis–haptotaxis model of parabolic–parabolic–ODE type

This paper deals with the boundedness of solutions to the following quasilinear chemotaxis–haptotaxis model of parabolic–parabolic–ODE type:

Authors: Long Lei and Zhongping Li

A study on the thermoelasticity of three-phase-lag dipolar materials with voids

With a wide applicability in solid state mechanics, the theory of continuous dipolar materials with voids is a distinctive part of microstructure theory, a theory that emerged with the necessity of eliminating...

Authors: Lavinia Codarcea-Munteanu and Marin Marin

Multiple positive solutions for quasilinear elliptic problems with combined critical Sobolev–Hardy terms

In this paper, we investigate the quasilinear elliptic equations involving multiple critical Sobolev–Hardy terms with Dirichlet boundary conditions on bounded smooth domains  ...

Authors: Yuanyuan Li

Existence of nonconstant periodic solutions for \(p(t)\)-Laplacian Hamiltonian system

Authors: Yuanfang Ru and Fanglei Wang

Qualitative properties for a pseudo-parabolic equation with nonlocal reaction term

This paper deals with the qualitative properties of solutions for null Neumann initial boundary value problem to a nonlocal pseudo-parabolic equation in the sense of ...

Authors: Yadong Zheng and Zhong Bo Fang

Local pseudo almost automorphic functions with applications to semilinear dynamic equations on changing-periodic time scales

In this paper, based on the concepts of changing-periodic time scales, we introduce a notion of local pseudo almost automorphic functions on an arbitrary time scale with a bounded graininess function μ. Then, som...

Authors: Chao Wang, Ravi P. Agarwal, Donal O’Regan and Rathinasamy Sakthivel

Direct and inverse problem for geometric perturbation of the Laplace operator in a strip

This paper is concerned with the inverse problem of determining geometric shape of a part γ of the boundary of a perturbed strip Ω from a pair of Cauchy data of a harmonic function u in Ω. This leads to the study...

Authors: I. Khélifa and L. Chorfi

Construction of singular limits for a strongly perturbed four-dimensional Navier problem with exponentially dominated nonlinearity and nonlinear terms

Authors: Sami Baraket, Souhail Chebbi and Nejmeddine Chorfi

A reduced fourth-order compact difference scheme based on a proper orthogonal decomposition technique for parabolic equations

In this paper, we present a reduced high-order compact finite difference scheme for numerical solution of the parabolic equations. CFDS4 is applied to attain high accuracy for numerical solution of parabolic e...

Authors: Baozou Xu and Xiaohua Zhang

Stability and Hopf bifurcation of a predator-prey model

In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method, we prove the stability of nonnegative equilibrium points. Secondly, we obtain...

Authors: Fan Wu and Yujuan Jiao

On an electrorheological fluid equation with orientated convection term

Authors: Huashui Zhan

Existence and uniqueness for some equation of a mixed elliptic-hyperbolic type

In the paper, we prove results on existence and uniqueness of weak solutions for closed Dirichlet problem for a transonic flow model, and interior regularity results are also given in the important special cas...

Authors: Zhang Haixia and Xiao Wei