Articles

Optimal lower bound for the first eigenvalue of fourth order measure differential equation

In this paper, we will find an explicit optimal lower bound for the first eigenvalue of a fourth order measure differential equation, motivated by physical problems when some physically meaningful measurement ...

Authors: Zhou Lijuan and Meng Gang

Existence and asymptotic analysis of positive solutions for a singular fractional differential equation with nonlocal boundary conditions

In this paper, we focus on the existence and asymptotic analysis of positive solutions for a class of singular fractional differential equations subject to nonlocal boundary conditions. By constructing suitabl...

Authors: Jianxin He, Xinguang Zhang, Lishan Liu, Yonghong Wu and Yujun Cui

Homoclinic solutions for second-order Hamiltonian systems with periodic potential

Authors: Yiwei Ye

Positive periodic solutions for nonlinear first-order delayed differential equations at resonance

Authors: Ruipeng Chen and Xiaoya Li

Multiplicity results for the Kirchhoff type equation via critical groups

In this paper, we will compute critical groups at zero for the Kirchhoff type equation using the property that critical groups are invariant under homotopies preserving isolatedness of critical points. Using t...

Authors: Zhenting Wang, Mingzheng Sun, Yutong Chen and Leiga Zhao

Inhomogeneous boundary value problems for steady compressible magnetohydrodynamic equations

This paper will be concerned with the compressible perturbation to steady magnetohydrodynamic equations near a uniform flow. In particular, the velocity of the basic flow under consideration can be any non-zer...

Authors: Chunhui Zhou

Fast homoclinic solutions for damped vibration problems with superquadratic potentials

In this paper we investigate the existence and multiplicity of homoclinic solutions for the following damped vibration problem:

Authors: Xinhe Zhu and Ziheng Zhang

Topological properties of \(C^{0}\)-solution set for impulsive evolution inclusions

Authors: Lu Zhang, Yong Zhou and Bashir Ahmad

Superlinear Kirchhoff-type problems of the fractional p-Laplacian without the (AR) condition

Authors: Jiabin Zuo, Tianqing An and Mingwei Li

Well-posedness of a higher-order Schrödinger–Poisson–Slater system

In this paper, we show the global well-posedness of a higher-order nonlinear Schrödinger equation. Specifically, we consider a system of infinitely many coupled higher-order Schrödinger–Poisson–Slater equation...

Authors: Saber Trabelsi

Blow-up rates and uniqueness of entire large solutions to a semilinear elliptic equation with nonlinear convection term

Authors: Bo Li and Haitao Wan

Periodic solution for second-order impulsive differential inclusions with relativistic operator

In this paper, the boundary value problem of a second-order impulsive differential inclusion involving a relativistic operator is studied. First, the singular problem is reduced to an equivalent non-singular p...

Authors: Suiming Shang, Zhanbing Bai, Yu Tian and Yue Yue

Oscillation theorems for nonlinear fractional difference equations

In this study, we discuss some theorems related to the oscillatory behavior of nonlinear fractional difference equations equipped with well-known fractional Riemann–Liouville difference operator. Then we give ...

Authors: Hakan Adiguzel

On the Darboux problem involving the distributional Henstock–Kurzweil integral

In this paper, we apply the method associated with the technique of measure of noncompactness and the Darbo fixed point theorem to study the existence of solutions of the Darboux problem involving the distribu...

Authors: Guoju Ye, Rong Cheng, Wei Liu and Hui Mei

Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem

In this manuscript, we give some sufficient conditions for existence, uniqueness and various kinds of Ulam stability for a toppled system of fractional order boundary value problems involving the Riemann–Liouv...

Authors: Zeeshan Ali, Akbar Zada and Kamal Shah

Existence and uniqueness for a kind of nonlocal fractional evolution equations on the unbounded interval

By means of a Laplace transform and its inverse transform, we obtain a correct equivalent integral equation for some kind of nonlocal abstract differential equations (fractional order) on the right half-axis. ...

Authors: Zhanmei Lv, Yanping Gong and Yi Chen

Low order nonconforming finite element method for time-dependent nonlinear Schrödinger equation

Authors: Chao Xu, Jiaquan Zhou, Dongyang Shi and Houchao Zhang

Topological structure of solution sets for fractional evolution inclusions of Sobolev type

The paper is devoted to establishing the solvability and topological property of solution sets for the fractional evolution inclusions of Sobolev type. We obtain the existence of mild solutions under the weake...

Authors: Pengxian Zhu and Qiaomin Xiang

An exact bifurcation diagram for a reaction–diffusion equation arising in population dynamics

Authors: Jerome Goddard II, Quinn A. Morris, Stephen B. Robinson and Ratnasingham Shivaji

Periodic boundary value problems for two classes of nonlinear fractional differential equations

By using the coincidence degree theorem, we obtain a new result on the existence of solutions for a class of fractional differential equations with periodic boundary value conditions, where a certain nonlinear...

Authors: Wenjuan Yao, Zhichang Guo and Jiebao Sun

A new approach of superconvergence analysis of a low order nonconforming MFEM for reaction–diffusion equation

Authors: Houchao Zhang and An Wang

Nonexistence of stable solutions for quasilinear Schrödinger equation

Authors: Lijuan Chen, Caisheng Chen, Hongwei Yang and Hongxue Song

Limiting behavior of blow-up solutions for the cubic nonlinear beam equation

In terms of the sharp Gagliardo–Nirenberg–Sobolev inequalities, we find the precisely sharp criteria of blow-up and global existence for the cubic nonlinear beam equations with ...

Authors: Pengshe Zheng and Lihui Leng

Asymptotic behavior of the solution of a queueing system modeled by infinitely many partial differential equations with integral boundary conditions

By studying the spectrum on the imaginary axis of the underlying operator, which corresponds to the M/G/1 retrial queueing model with general retrial times described by infinitely many partial differential equ...

Authors: Nurehemaiti Yiming and Geni Gupur

Existence results for impulsive semilinear differential inclusions with nonlinear boundary conditions

In this paper, we discuss the nonlinear boundary problem for first-order impulsive semilinear differential inclusions. We establish existence results by using Martelli’s fixed point theorem with upper and lowe...

Authors: Yan Luo

Weighted integral inequality and applications in general energy decay estimate for a variable density wave equation with memory

This paper develops a weighted integral inequality to derive decay estimates for the quasilinear viscoelastic wave equation with variable density

Authors: Fushan Li and Fengying Hu

A class of second-order nonlocal indefinite impulsive differential systems

Authors: Lishuai Jiao and Xuemei Zhang

Dynamics of a predator–prey system with three species

This paper is concerned with the dynamics of a predator–prey system with three species. When the domain is bounded, the global stability of positive steady state is established by contracting rectangles. When ...

Authors: Zhifang Bi and Shuxia Pan

Global existence of solutions for a class of thermoelastic plate systems

This paper is concerned with the initial-boundary value problem for a class of thermoelastic plate systems. Under some appropriate assumptions, the global existence of solutions is obtained.

Authors: Yang Liu

Existence of stable standing waves for the Schrödinger–Choquard equation

Authors: Kun Liu and Cunqin Shi

Existence of nontrivial solutions for a class of nonlocal Kirchhoff type problems

With the aid of the three-critical-point theorem due to Brezis and Nirenberg (see Brezis and Nirenberg in Commun. Pure Appl. Math. 44:939–963, 1991), two existence results of at least two nontrivial solutions for...

Authors: Zeng-Qi Ou and Chun Li

Blow-up phenomena and lifespan for a quasi-linear pseudo-parabolic equation at arbitrary initial energy level

Authors: Gongwei Liu and Ruimin Zhao

Existence of the classical and strong solutions for fractional semilinear initial value problems

We prove the existence and uniqueness of classical and strong solutions of a fractional semilinear evolution equation using the method of a semigroup and the Banach fixed theorem.

Authors: A. Al-Omari and H. Al-Saadi

Mid-knot cubic non-polynomial spline for a system of second-order boundary value problems

In this paper, a mid-knot cubic non-polynomial spline is applied to obtain the numerical solution of a system of second-order boundary value problems. The numerical method is proved to be uniquely solvable and it...

Authors: Qinxu Ding and Patricia J. Y. Wong

Existence of multiple positive solutions to integral boundary value systems with boundary multiparameters

We establish the existence, nonexistence, and multiplicity of positive solutions to semilinear elliptic systems with integral boundary conditions when positive multiparameters vary on the boundary. We prove th...

Authors: Eunkyung Ko and Eun Kyoung Lee

Existence of solutions for perturbed fractional equations with two competing weighted nonlinear terms

This paper deals with a perturbed nonlocal equation of fractional Laplacian type involving two competing nonlinear terms with weights f and h. Under two kinds of integrability conditions on the ratio of f to h, w...

Authors: Yujuan Tian and Shasha Zhao

Existence of solution for integral boundary value problems of fractional differential equations

Authors: Xueying Yue and Kemei Zhang

Study of a generalized logistic equation with nonlocal reaction term

Authors: Jianhua Zhou, Ge Gao and Baoqiang Yan

Solutions for a class of fractional Langevin equations with integral and anti-periodic boundary conditions

In this paper, we consider a class of fractional Langevin equations with integral and anti-periodic boundary conditions. By using some fixed point theorems and the Leray–Schauder degree theory, several new exi...

Authors: Zongfu Zhou and Yan Qiao

General decay and blow-up of solutions for a nonlinear viscoelastic wave equation with strong damping

This article is concerned with the decay and blow-up properties of a nonlinear viscoelastic wave equation with strong damping. We first show a local existence theorem. Then, we prove the global existence of so...

Authors: Qian Li and Luofei He

On a \(p(x)\)-biharmonic problem with Navier boundary condition

Authors: Zheng Zhou

Nonlinear Rosseland thermal radiation and energy dissipation effects on entropy generation in CNTs suspended nanofluids flow over a thin needle

In this paper, we examine thermal radiation effect of the nonlinear form on the dissipative nanofluids containing carbon nanotubes past a moving horizontal thin needle. We also perform a second law analysis wi...

Authors: Muhammad Idrees Afridi, Iskander Tlili, Muhammad Qasim and Ilyas Khan

Robust exponential attractors for a parabolic–hyperbolic phase-field system

In this paper, we construct a robust family of exponential attractors for a parabolic–hyperbolic phase-field system (PHPFS), which describes phase separation in material sciences, e.g., melting and solidificat...

Authors: Cyril D. Enyi

Multiplicity of solutions for a quasilinear elliptic equation with \((p,q)\)-Laplacian and critical exponent on \(\mathbb{R}^{N}\)

Authors: Chen Huang, Gao Jia and Tiansi Zhang

The stability of solutions for the Fornberg–Whitham equation in \(L^{1}(\mathbb{R})\) space

Authors: Xiujuan Gao, Shaoyong Lai and Hongjin Chen

On decay and blow-up of solutions for a nonlinear beam equation with double damping terms

Authors: Jiali Yu, Yadong Shang and Huafei Di

The asymptotic limits of Riemann solutions for the isentropic extended Chaplygin gas dynamic system with the vanishing pressure

We construct the solutions to the Riemann problem for the isentropic extended Chaplygin gas dynamic system for all kinds of situations by the phase plane analysis. We investigate the asymptotic limits of solut...

Authors: Meizi Tong, Chun Shen and Xiuli Lin

Properties of solutions for a reaction–diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition

In this paper, the authors consider the reaction–diffusion equation with nonlinear absorption and nonlinear nonlocal Neumann boundary condition. They prove that the solution either exists globally or blows up ...

Authors: Jian Wang and Hui Yang

Small-amplitude nonlinear periodic oscillations in a suspension bridge system

This paper deals with a coupled nonlinear beam-wave system, proposed by Lazer and McKenna, modeling a suspension bridge. By constructing a suitable Nash–Moser-type iteration scheme, the existence of small-ampl...

Authors: Hengyan Li and Xin Zhao

Fixed point theorems for a class of nonlinear sum-type operators and application in a fractional differential equation

Authors: Hui Wang, Lingling Zhang and Xiaoqiang Wang