Articles

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

The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

Authors: Limei Dai and Huihui Cheng

Uniform estimates with data from generalized Lebesgue spaces in periodic structures

We study various types of uniform Calderón–Zygmund estimates for weak solutions to elliptic equations in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term from we...

Authors: Yunsoo Jang

Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in

Authors: Yuanfei Li, Shuanghu Zhang and Changhao Lin

Ground state solutions for Kirchhoff-type equations with general nonlinearity in low dimension

Authors: Jing Chen and Yiqing Li

A study on controllability of impulsive fractional evolution equations via resolvent operators

In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theor...

Authors: Haide Gou and Yongxiang Li

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

This article has been retracted. Please see the Retraction Notice for more detail: https://​doi.​org/​10.​1186/​s13661-021-01502-z

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

Regularity criterion for 3D nematic liquid crystal flows in terms of finite frequency parts in \(\dot{B}_{\infty,\infty }^{-1}\)

Authors: Xiaoli Chen and Haiyan Cheng

Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

In this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parame...

Authors: S. Heidari and A. Razani

Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incom...

Authors: Xiaoyuan Wang, Sirui Li and Tingting Wang

Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems t...

Authors: Yanbin Sang and Luxuan He

First order differential systems with a nonlinear boundary condition via the method of solution-regions

In this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

Authors: Marlène Frigon, Marcos Tella and F. Adrián F. Tojo

Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

We study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

Authors: Lifang Fu and Mingzheng Sun

On a doubly degenerate parabolic equation with a nonlinear damping term

Authors: Wenbin Xu

New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

A type of non-Newtonian filtration equations with variable delay is considered. Using a new approach which was established by Ge and Ren in (Nonlinear Anal. 58:477–488, 2004), we obtain the existence of periodic ...

Authors: Mei Xu and Bo Du

Analysis of reaction–diffusion systems where a parameter influences both the reaction terms as well as the boundary

Authors: A. Acharya, N. Fonseka and R. Shivaji

Random attractor for second-order stochastic delay lattice sine-Gordon equation

Authors: Xintao Li, Lianbing She and Zhenpei Shan

Positive ground states for nonlinearly coupled Choquard type equations with lower critical exponents

Authors: Huiling Wu

Dynamic analysis of a stochastic four species food-chain model with harvesting and distributed delay

A stochastic four species food-chain model is proposed in this paper. Here, artificial harvest in each species and the effect of time delay for interaction between species are considered, which makes the model...

Authors: Nafeisha Tuerxun, Zhidong Teng and Wei Chen

On Neumann problem for the degenerate Monge–Ampère type equations

Authors: Juhua Shi and Feida Jiang

Long-time behavior of solutions for a fractional diffusion problem

This paper deals with the asymptotic behavior of solutions to the initial-boundary value problem of the following fractional p-Kirchhoff equation:

Authors: Ailing Qi, Die Hu and Mingqi Xiang

Retraction Note: Existence of global solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s13661-021-01488-8

Authors: Zhen Liu