Articles

The entropy weak solution to a generalized Fornberg–Whitham equation

Authors: Nan Li and Shaoyong Lai

Unique identification of a multi-layered fluid–solid medium

This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid–solid medium in the three dimensional space. We establish the global uniqueness in identifying...

Authors: Yanli Cui, Xiliang Li and Fenglong Qu

Retraction Note: Boundary behaviors of modified Green’s function with respect to the stationary Schrödinger operator and its applications

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with a number of previously published articles from different authors [2–4]. The author has not responded to any correspon...

Authors: Zhiqiang Li

Zero Mach number limit of the compressible Euler–Korteweg equations

In this paper, we investigate the zero Mach number limit for the three-dimensional compressible Euler–Korteweg equations in the regime of smooth solutions. Based on the local existence theory of the compressib...

Authors: Yeping Li and Gang Zhou

Study of impulsive fractional differential equation under Robin boundary conditions by topological degree method

This research work is dedicated to investigating a class of impulsive fractional order differential equations under the Robin boundary conditions via the application of topological degree theory (TDT). We esta...

Authors: Atta Ullah, Kamal Shah, Thabet Abdeljawad, Rahmat Ali Khan and Ibrahim Mahariq

Nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions and Ulam–Hyers stability

In this paper, we study a nonlinear fractional differential equation involving two mixed fractional orders with nonlocal boundary conditions. By using some new techniques, we introduce a formula of solutions f...

Authors: Fang Li, Wenjing Yang and Huiwen Wang

Renormalization for the Laplacian and global well-possness of the Landau–Lifshitz–Gilbert equation in dimensions \(n \geq3\)

Authors: Penghong Zhong, Fengong Wu and Shengxiang Tang

Attractors for the nonclassical reaction–diffusion equations on time-dependent spaces

Authors: Kaixuan Zhu, Yongqin Xie and Feng Zhou

The spectral implementation of the nonstationary Stokes problem with nonstandard boundary conditions

This paper deals with the implementation of the spectral discretization of the vorticity–velocity–pressure formulation of the nonstationary Stokes problem. We use the implicit Euler scheme for the discretizati...

Authors: Mohamed Abdelwahed, Nejmeddine Chorfi and Henda Ouertani

An application of Phragmén–Lindelöf theorem to the existence of ground state solutions for the generalized Schrödinger equation with optimal control

In this paper, we develop optimal Phragmén–Lindelöf methods, based on the use of maximum modulus of optimal value of a parameter in a Schrödinger functional, by applying the Phragmén–Lindelöf theorem for a sec...

Authors: Chaofeng Zhang and Rong Hu

Well-posedness of a Neumann-type problem on a gauge ball in H-type groups

We discuss the existence and uniqueness of solution for the second boundary value problem of potential theory often referred to as the Neumann problem, on a gauge ball for the canonical sub-Laplacian in H-type gr...

Authors: Mukund Madhav Mishra and Ashutosh Pandey

A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation

In this paper, a fast multiscale Galerkin algorithm is developed for solving the boundary value problem of the fractional Bagley–Torvik equation. For this purpose, we employ multiscale orthogonal functions hav...

Authors: Jian Chen

Global existence and exponential decay of solutions for generalized coupled non-degenerate Kirchhoff system with a time varying delay term

The paper studies a system of nonlinear viscoelastic Kirchhoff system with a time varying delay and general coupling terms. We prove the global existence of solutions in a bounded domain using the energy and F...

Authors: Nadia Mezouar and Salah Boulaaras

Positive periodic solution for prescribed mean curvature generalized Liénard equation with a singularity

The main purpose of this paper is to investigate the existence of a positive periodic solution for a prescribed mean curvature generalized Liénard equation with a singularity (weak and strong singularities of ...

Authors: Yun Xin and Zhibo Cheng

Existence of positive radial solution for Neumann problem on the Heisenberg group

Authors: F. Safari and A. Razani

Coupled elliptic systems depending on the gradient with nonlocal BCs in exterior domains

We study the existence and multiplicity of positive radial solutions for a coupled elliptic system in exterior domains where the nonlinearities depend on the gradients and the boundary conditions are nonlocal....

Authors: Filomena Cianciaruso, Luigi Muglia and Paolamaria Pietramala

Retraction Note: Boundary value behaviors for solutions of the equilibrium equations with angular velocity

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article from other authors that was simultaneously under consideration at another journal [2]. Additionally, the a...

Authors: Jiaofeng Wang, Jun Pu, Bin Huang and Guojian Shi

Initial boundary value problem for generalized Zakharov equations with nonlinear function terms

In this paper, we consider the initial boundary value problem for generalized Zakharov equations. Firstly, we prove the existence and uniqueness of the global smooth solution to the problem by a priori integra...

Authors: Xueqin Wang, Yadong Shang and Chunlin Lei

Stability result of a viscoelastic plate equation with past history and a logarithmic nonlinearity

In this paper, we are concerned with the decay rate of the solution of a viscoelastic plate equation with infinite memory and logarithmic nonlinearity. We establish an explicit and general decay rate results w...

Authors: Adel M. Al-Mahdi

Affine-periodic solutions by asymptotic and homotopy equivalence

Authors: Jiamin Xing and Xue Yang

Existence of positive solutions to negative power nonlinear integral equations with weights

Authors: Hang Chen, Qianqiao Guo and Qian Wang

Nonexistence and existence of positive radial solutions to a class of quasilinear Schrödinger equations in \(\mathbb{R}^{N}\)

Authors: Jing Li and Ying Wang

Approximate solutions for HBV infection with stability analysis using LHAM during antiviral therapy

Hepatitis B virus (HBV) is a life-threatening virus that causes very serious liver-related diseases from the family of Hepadnaviridae having very rare qualities resembling retroviruses. In this paper, we analy...

Authors: M. Aniji, N. Kavitha and S. Balamuralitharan

Pullback attractor of a non-autonomous order-2γ parabolic equation for an epitaxial thin film growth model

Authors: Xiaojie Yang, Hui Liu and Chengfeng Sun

Retraction Note: Levin’s type boundary behaviors for functions harmonic and admitting certain lower bounds

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with a previously published article by Pang et al. [2]. The article also shows evidence of authorship manipulation. The id...

Authors: Zhiqiang Li and Mohamed Vetro

Invariant tori of full dimension for higher-dimensional beam equations with almost-periodic forcing

Authors: Jie Rui and Yi Wang

Lower bound for the blow-up time for a general nonlinear nonlocal porous medium equation under nonlinear boundary condition

Authors: Baiping Ouyang, Yiwu Lin, Yan Liu and Zihan Cai

Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions

In this article, we study a modified maximum principle approach under condition on the weight of the delay term in the feedback and the weight of the term without delay. On that basis, we prove the existence o...

Authors: Yisheng Hu, Songhai Qin, Zhibin Liu and Yi Wang

The asymptotic behavior of the stochastic coupled Kuramoto–Sivashinsky and Ginzburg–Landau equations

The stochastic coupled Kuramoto–Sivashinsky and Ginzburg–Landau equations (KS-GL) perturbed by additive noises is investigated in this paper. By making careful analysis, we first consider the existence and uni...

Authors: Lin Lin and Mei Li

Multiplicity and existence of solutions for generalized quasilinear Schrödinger equations with sign-changing potentials

Authors: Chen Huang

Existence and uniqueness of mild solutions to the chemotaxis-fluid system modeling coral fertilization

In this paper, we consider the egg-sperm chemotaxis model of coral with the incompressible fluid equations in the whole space. The existence of global mild solutions in scaling invariant spaces is proved with ...

Authors: Die Hu, Peng Chen and Deyi Ma

Dynamic analysis of a complex system under preemptive repeat repair discipline

This paper considers a two-unit complex system, in which one of the components has priority with preemptive repeat repair disciplines, described by partial differential equations with integral boundary conditi...

Authors: Ehmet Kasim and Geni Gupur

Response solution to complex Ginzburg–Landau equation with quasi-periodic forcing of Liouvillean frequency

In this paper, the existence of a response solution with the Liouvillean frequency vector to the quasi-periodically forced complex Ginzburg–Landau equation, whose linearized system is elliptic–hyperbolic, is o...

Authors: Shimin Wang and Jie Liu

The nonnegative weak solution of a degenerate parabolic equation with variable exponent growth order

Authors: Huashui Zhan

Global and blow-up solutions for a nonlinear reaction diffusion equation with Robin boundary conditions

In the paper, we investigate global and blow-up solutions for a class of nonlinear reaction diffusion equations with Robin boundary conditions. By using auxiliary functions and a first-order differential inequ...

Authors: Huimin Tian and Lingling Zhang

Nontrivial solutions of a class of fractional differential equations with p-Laplacian via variational methods

In this paper, a class of boundary value problems for fractional differential equations with a parameter is studied via the variational methods. Firstly, we present a result that the boundary value problems ha...

Authors: Yan Qiao, Fangqi Chen and Yukun An

Existence and concentration of positive solutions for a class of discontinuous quasilinear Schrödinger problems in \(\mathbb{R}^{N}\)

In this paper, a class of quasilinear Schrödinger equations with discontinuous nonlinearity is considered. After changing variables, by using nonsmooth critical point theory, we obtain the existence and concen...

Authors: Ziqing Yuan

Non-existence for a semi-linear fractional system with Sobolev exponents via direct method of moving spheres

Authors: Xiaoxue Ji and Pengcheng Niu

A hybrid Caputo fractional modeling for thermostat with hybrid boundary value conditions

We provide an extension for the second-order differential equation of a thermostat model to the fractional hybrid equation and inclusion versions. We consider boundary value conditions of this problem in the f...

Authors: Dumitru Baleanu, Sina Etemad and Shahram Rezapour

Multiple solutions for fractional p-Laplace equation with concave-convex nonlinearities

Authors: Qiang Chen, Caisheng Chen and Yanling Shi

A general stability result for second order stochastic quasilinear evolution equations with memory

The goal of this paper is to discuss an initial boundary value problem for the stochastic quasilinear viscoelastic evolution equation with memory driven by additive noise. We prove the existence of global solu...

Authors: Hui Yang, Shiyue Fang, Fei Liang and Min Li

Finite time blow-up for the nonlinear Schrödinger equation in trapped dipolar quantum gases with arbitrarily positive initial energy

Authors: Yi Yuan and Binhua Feng

Remarks on infinitely many solutions for a class of Schrödinger equations with sign-changing potential

Authors: Rong Cheng and Yijia Wu

Blow-up analysis for two kinds of nonlinear wave equations

Authors: Hengyan Li, Junling Sun and Xin Zhao

Pullback attraction in \(H_{0}^{1}\) for semilinear heat equation in expanding domains

Authors: Yanping Xiao, Yuqin Bai and Huanhuan Zhang

Existence of solution for a quasilinear elliptic Neumann problem involving multiple critical exponents

In this paper, we study the Neumann boundary value problem to a quasilinear elliptic equation with the critical Sobolev exponent and critical Hardy–Sobolev exponent, and prove the existence of nontrivial nonne...

Authors: Yuanxiao Li and Xiying Wang

On a Schrödinger–Poisson system with singularity and critical nonlinearities

In this paper, we study the Schrödinger–Poisson system with singularity and critical growth terms. By means of variational methods with an appropriate truncation argument, the existence and multiplicity of pos...

Authors: Zhipeng Cai, Chunyu Lei and Changmu Chu

Null controllability of a semilinear degenerate parabolic equation with a gradient term

This paper concerns the null controllability of a semilinear control system governed by degenerate parabolic equation with a gradient term, where the nonlinearity of the problem is involved with the first deri...

Authors: Fengdan Xu, Qian Zhou and Yuanyuan Nie

Dynamics and oscillations of models for differential equations with delays

By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of ...

Authors: Mohsen Miraoui and Dušan D. Repovš

Analysis of a time-delayed free boundary problem for solid tumor growth with angiogenesis and direct influence of inhibitors

In this paper we consider a free boundary problem for tumor growth under direct effect of inhibitors with angiogenesis and time delays in proliferation. The existence and uniqueness of the steady state solutio...

Authors: Shihe Xu and Dan Su