Articles

Multiple solutions for singular semipositone boundary value problems of fourth-order differential systems with parameters

The aim of this paper is to establish some results about the existence of multiple solutions for the following singular semipositone boundary value problem of fourth-order differential systems with parameters:

Authors: Longfei Lin, Yansheng Liu and Daliang Zhao

Multiple solutions for a quasilinear Schrödinger–Poisson system

Authors: Jing Zhang

Asymptotic behavior for a viscoelastic Kirchhoff equation with distributed delay and Balakrishnan–Taylor damping

A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

Authors: Abdelbaki Choucha and Salah Boulaaras

Radial solutions for fully nonlinear elliptic equations of Monge–Ampère type

First, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetr...

Authors: Limei Dai, Huihui Cheng and Hongfei Li

Effect of the protection zone in a diffusive ratio-dependent predator–prey model with fear and Allee effect

In this paper, we study the influence of a protection zone for the prey on a diffusive predator–prey model with fear factor and Allee effect. The prior estimate, global existence, nonexistence of nonconstant p...

Authors: Huan Wang and Hui Xing

Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

Authors: Jian Zhou and Yunshun Wu

A fractional differential equation with multi-point strip boundary condition involving the Caputo fractional derivative and its Hyers–Ulam stability

In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing ...

Authors: Mehboob Alam, Akbar Zada, Ioan-Lucian Popa, Alireza Kheiryan, Shahram Rezapour and Mohammed K. A. Kaabar

A note on global existence of strong solution to the 3D micropolar equations with a damping term

Authors: Wen Wang and Yunchong Long

Existence and uniqueness of a finite energy solution for the mixed value problem of porous thermoelastic bodies

We consider the mixed problem with boundary and initial data in thermoelasticity of porous bodies with dipolar structure. By generalizing some known results developed by Dafermos in a more simple case of the c...

Authors: M. Marin, S. Vlase and C. Carstea

Well posedness of a nonlinear mixed problem for a parabolic equation with integral condition

The aim of this work is to prove the well posedness of some posed linear and nonlinear mixed problems with integral conditions. First, an a priori estimate is established for the associated linear problem and ...

Authors: Abdelkader Djerad, Ameur Memou and Ali Hameida

On Green’s function of Cauchy–Dirichlet problem for hyperbolic equation in a quarter plane

The definition of a Green’s function of a Cauchy–Dirichlet problem for the hyperbolic equation in a quarter plane is given. Its existence and uniqueness have been proven. Representation of the Green’s function...

Authors: Makhmud Sadybekov and Bauyrzhan Derbissaly

Nonlocal Lazer–McKenna-type problem perturbed by the Hardy’s potential and its parabolic equivalence

In this paper, we study the effect of Hardy potential on the existence or nonexistence of solutions to the following fractional problem involving a singular nonlinearity:

Authors: Masoud Bayrami-Aminlouee, Mahmoud Hesaaraki, Mohamed Karim Hamdani and Nguyen Thanh Chung

Some properties of implicit impulsive coupled system via φ-Hilfer fractional operator

The major goal of this work is investigating sufficient conditions for the existence and uniqueness of solutions for implicit impulsive coupled system of φ-Hilfer fractional differential equations (FDEs) with ins...

Authors: Mohammed A. Almalahi and Satish K. Panchal

Nonlinear differential equations with perturbed Dirichlet integral boundary conditions

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied probl...

Authors: Alberto Cabada and Javier Iglesias

Retraction Note: New applications of Schrödingerean Green potential to boundary behaviors of superharmonic functions

Authors: Kai Lai, Jing Mu and Hong Wang

Implicit nonlinear fractional differential equations of variable order

In this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to...

Authors: Amar Benkerrouche, Mohammed Said Souid, Kanokwan Sitthithakerngkiet and Ali Hakem

Blow-up for a viscoelastic von Karman equation with strong damping and variable exponent source terms

In this article, we deal with a strongly damped von Karman equation with variable exponent source and memory effects. We investigate blow-up results of solutions with three levels of initial energy such as non...

Authors: Sun-Hye Park

A new blow up criterion for the 3D magneto-micropolar fluid flows without magnetic diffusion

This note obtains a new regularity criterion for the three-dimensional magneto-micropolar fluid flows in terms of one velocity component and the gradient field of the magnetic field. The authors prove that the...

Authors: Dongxiang Chen and Qifeng Liu

A blow-up result for a system of coupled viscoelastic equations with arbitrary positive initial energy

This article is devoted to a study of the blow-up result for a system of coupled viscoelastic wave equations. By establishing a new auxiliary function and using the reduction to absurdity method, we obtain som...

Authors: Qian Li

Three new approaches for solving a class of strongly nonlinear two-point boundary value problems

Three new and applicable approaches based on quasi-linearization technique, wavelet-homotopy analysis method, spectral methods, and converting two-point boundary value problem to Fredholm–Urysohn integral equa...

Authors: Monireh Nosrati Sahlan and Hojjat Afshari

Global solutions of wave equations with multiple nonlinear source terms under acoustic boundary conditions

Under the acoustic boundary conditions, the initial boundary value problem of a wave equation with multiple nonlinear source terms is considered. This paper gives the energy functional of regular solutions for...

Authors: Shoubo Jin and Jian Li

Construct new type solutions for the fractional Schrödinger equation

Authors: Yuan Lin and Weiming Liu

Free convection inside a porous square cavity with convective boundary condition using spline functions

In this paper, we consider the problem of free convection in a square cavity filled with a porous medium with convective boundary condition on the left wall of the cavity. We first transform the governing equa...

Authors: Sanda Micula and Ioan Pop

Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor

Authors: Yonghai Wang, Minhui Hu and Yuming Qin

New multiplicity of positive solutions for some class of nonlocal problems

Authors: Zhigao Shi and Xiaotao Qian

Retraction Note: A remark on the a-minimally thin sets associated with the Schrödinger operator

Authors: Gaixian Xue

Normal periodic solutions for the fractional abstract Cauchy problem

Authors: Jennifer Bravo and Carlos Lizama

On instability of Rayleigh–Taylor problem for incompressible liquid crystals under \(L^{1}\)-norm

We investigate the nonlinear Rayleigh–Taylor (RT) instability of a nonhomogeneous incompressible nematic liquid crystal in the presence of a uniform gravitational field. We first analyze the linearized equatio...

Authors: Mengmeng Liu and Xueyun Lin

Retraction Note: Existence results for the general Schrödinger equations with a superlinear Neumann boundary value problem

Authors: Zhen Liu

Application of the topological sensitivity method to the reconstruction of plasma equilibrium domain in a tokamak

The topological sensitivity method is an optimization technique used in different inverse problem solutions. In this work, we adapt this method to the identification of plasma domain in a Tokamak. An asymptoti...

Authors: Mohamed Abdelwahed, Nejmeddine Chorfi, Maatoug Hassine and Imen Kallel

Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent

In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solut...

Authors: Hongsen Fan and Zhiying Deng

A new method for high-order boundary value problems

This paper presents a numerical algorithm for solving high-order BVPs. We introduce the construction method of multiscale orthonormal basis in

Authors: Yingchao Zhang, Liangcai Mei and Yingzhen Lin

Correctness conditions for high-order differential equations with unbounded coefficients

We give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for...

Authors: Kordan N. Ospanov

Structural stability for the Forchheimer equations interfacing with a Darcy fluid in a bounded region in \(\mathbb{R}^{3}\)

Authors: Jincheng Shi and Yan Liu

Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials

Authors: Yan Meng, Xianjiu Huang and Jianhua Chen

Infinite number of solutions for some elliptic eigenvalue problems of Kirchhoff-type with non-homogeneous material

In this paper, using variational method, we study the existence of an infinite number of solutions (some are positive, some are negative, and others are sign-changing) for a non-homogeneous elliptic Kirchhoff ...

Authors: Baoqiang Yan, Donal O’Regan and Ravi P. Agarwal

Multivalued nonmonotone dynamic boundary condition

In this paper, we introduce a new class of hemivariational inequalities, called dynamic boundary hemivariational inequalities, reflecting the fact that the governing operator is also active on the boundary. In...

Authors: Khadija Aayadi, Khalid Akhlil, Sultana Ben Aadi and Mourad El Ouali

Bifurcation analysis in a diffusive phytoplankton–zooplankton model with harvesting

A diffusive phytoplankton–zooplankton model with nonlinear harvesting is considered in this paper. Firstly, using the harvesting as the parameter, we get the existence and stability of the positive steady stat...

Authors: Yong Wang

Linear stability of blowup solution of incompressible Keller–Segel–Navier–Stokes system

Authors: Yan Yan and Hengyan Li

An oscillation theorem for the nonlinear degenerate elliptic equation in the Heisenberg group

Authors: Duan Wu and Pengcheng Niu

Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian

By employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give preci...

Authors: Shaohong Wang and Zhan Zhou

Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

In this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorem...

Authors: Jian Liu and Wenguang Yu

An inverse problem of reconstructing option drift rate from market observation data

Drift rate is a very important parameter in the evolution of stock price, which has significant impact on the corresponding option pricing. This paper deals with an inverse problem of recovering the drift func...

Authors: Z. C. Deng, X. Y. Zhao and L. Yang

Fujita type theorem for a class of coupled quasilinear convection–diffusion equations

In this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the in...

Authors: Yanan Zhou, Yan Leng and Yuanyuan Nie

New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

In this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and compar...

Authors: Osama Moaaz, Choonkil Park, Elmetwally M. Elabbasy and Waed Muhsin

Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

In the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using...

Authors: Cholticha Nuchpong, Sotiris K. Ntouyas, Devaraj Vivek and Jessada Tariboon

Traveling wave solutions for a class of reaction-diffusion system

In this paper we investigate the existence of traveling wave for a one-dimensional reaction diffusion system. We show that this system has a unique translation traveling wave solution.

Authors: Bingyi Wang and Yang Zhang

Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms

By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the pe...

Authors: Haiyan Lv and Guanwei Chen

Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, t...

Authors: Hong Qiu, Wenmin Deng and Mingqi Xiang

Uniqueness and concentration for a fractional Kirchhoff problem with strong singularity

Authors: Shengbin Yu and Jianqing Chen