Articles

Schrödinger-type identity to the existence and uniqueness of a solution to the stationary Schrödinger equation

In this article we study applications of the Schrödinger-type identity for obtaining transmutations via the fixed point index for nonlinear integral equations. It is possible to derive a wide range of transmut...

Authors: Delin Sun

The existence and Hyers–Ulam stability of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order \(1<\beta<2\)

This paper deals with the existence of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order ...

Authors: Yuchen Guo, Xiao-Bao Shu, Yongjin Li and Fei Xu

Liouville type theorem for a singular elliptic equation with finite Morse index

This paper considers the nonexistence of solutions for the following singular quasilinear elliptic problem:

Authors: Zonghu Xiu, Jing Zhao, Jianyi Chen and Hongwei Yang

Multiplicity of periodic bouncing solutions for generalized impact Hamiltonian systems

Authors: Delong Huang and Fei Guo

Multiplicity results for p-Laplacian boundary value problem with jumping nonlinearities

We investigate the multiplicity of solutions for one-dimensional p-Laplacian Dirichlet boundary value problem with jumping nonlinearities. We obtain three theorems: The first states that there exists exactly one ...

Authors: Tacksun Jung and Q-Heung Choi

Existence and asymptotic properties of positive solutions for a general quasilinear Schrödinger equation

By a change of variables with cut-off functions, we study the existence and the asymptotic behavior of positive solutions for a general quasilinear Schrödinger equation which arises from plasma physics. We ext...

Authors: Xiang Zhang and Yimin Zhang

A further study on the coupled Allen–Cahn/Cahn–Hilliard equations

In this paper, we will show that solutions of the initial boundary value problem for the coupled system of Allen–Cahn/Cahn–Hilliard equations continuously depend on parameters of the system, and under some res...

Authors: Jiaqi Yang and Changchun Liu

The obstacle problem for nonlinear noncoercive elliptic equations with \(L^{1}\)-data

Authors: Jun Zheng and Leandro S. Tavares

Retraction Note: Velocity and shear stress for an Oldroyd-B fluid within two cylinders

The Editors-in-Chief are retracting this article [1] because it overlaps with previously published articles [2,3]. None of the authors have responded to correspondence about this retraction.

Authors: Shin Min Kang, Waqas Nazeer, Muhammad Athar, Muhammad Danial Hisham and Young Chel Kwun

Laplace’s equation with concave and convex boundary nonlinearities on an exterior region

Authors: Jinxiu Mao, Zengqin Zhao and Aixia Qian

Multiplicity of solutions for a class of \((p_{1},p_{2},\ldots,p_{n})\)-Laplacian elliptic systems with a nonsmooth potential

Authors: Ziqing Yuan, Yan Wang and Sheng Liu

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

Authors: Yanbin Sang and Yan Ren

A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation

We study a new way to convergence results for a nonlinear hyperbolic equation with bilinear element. Such equation is transformed into a parabolic system by setting the original solution u as ...

Authors: Junjun Wang and Lijuan Guo

Forced oscillation of fractional differential equations via conformable derivatives with damping term

Based on the properties of nonlocal fractional calculus generated by conformable derivatives, we establish some sufficient conditions for oscillation of all solutions for fractional differential equations with...

Authors: Aphirak Aphithana, Sotiris K. Ntouyas and Jessada Tariboon

Boundary value problems of fractional q-difference equations on the half-line

In this paper, we consider the boundary value problem of a class of nonlinear fractional q-difference equations involving the Riemann–Liouville fractional q-derivative on the half-line. By means of Schauder fixed...

Authors: Kuikui Ma, Xinhui Li and Shurong Sun

Symmetries and conservation laws of the Yao–Zeng two-component short-pulse equation

This paper uses the Lie group method to analyze the symmetries of the Yao–Zeng two-component short-pulse equation which describes the propagation of polarized ultrashort light pulses in cubically nonlinear ani...

Authors: Ben Gao and Yao Zhang

Three-dimensional free convective flow of a second-grade fluid through a porous medium with periodic permeability and heat transfer

In this study, we model and theoretically analyze a free convective three-dimensional flow of an incompressible second-grade fluid through a highly porous medium bounded by an infinite vertical porous plate su...

Authors: M. A. Rana and A. Latif

Effects of melting process on the hydromagnetic wedge flow of a Casson nanofluid in a porous medium

An investigation is carried out to capture the influence of melting process and permeability of the medium on the hydromagnetic wedge flow of a Casson nanofluid. The effects of thermophoresis and Brownian moti...

Authors: Subharthi Sarkar and Mehari Fentahun Endalew

The local existence of strong solution for the stochastic 3D Boussinesq equations

Authors: Lihuai Du

Positive solutions of fourth-order problems with dependence on all derivatives in nonlinearity under Stieltjes integral boundary conditions

In this article, we investigate the existence of positive solutions to fourth-order problems with dependence on all derivatives in nonlinearities subject to the Stieltjes integral boundary conditions

Authors: Yuexiao Ma, Chenyang Yin and Guowei Zhang

The existence of positive solution for singular Kirchhoff equation with two parameters

Authors: Ke Di and Baoqiang Yan

Asymptotic solutions on multiple solutions arising from laminar flow in a uniformly porous channel with expanding or contracting walls

This paper is concerned with asymptotic solutions of a nonlinear boundary value problem which arises from laminar flow in a uniformly porous channel with expanding or contracting walls. For values of the wall ...

Authors: Qizheng Huang, Lin Li and Zigen Ouyang

On multipoint resonant problems on the half-line

In this work we obtain sufficient conditions for the existence of bounded solutions of a resonant multipoint second-order boundary value problem, with a fully differential equation.

Authors: Lucía López-Somoza and Feliz Minhós

Global existence and stability of a class of nonlinear evolution equations with hereditary memory and variable density

In this paper, we consider the initial boundary value problem of nonlinear evolution equation with hereditary memory, variable density, and external force term

Authors: Fushan Li and Zhiqiang Jia

New results on competition and cooperation model of two enterprises with multiple delays and feedback controls

In this paper, we put up and study a competition and cooperation model of two enterprises with multiple delays and feedback controls. A set of sufficient conditions which ensure the existence of periodic solut...

Authors: Changjin Xu, Peiluan Li, Qimei Xiao and Shuai Yuan

Sharp criteria of blow-up solutions for the cubic nonlinear beam equation

Authors: Jun Qing and Chuangyuan Zhang

Method of fundamental solutions for a Cauchy problem of the Laplace equation in a half-plane

This paper is to provide an analysis of an ill-posed Cauchy problem in a half-plane. This problem is novel since the Cauchy data on the accessible boundary is given, whilst the additional temperature is involv...

Authors: Bo Chen, Yao Sun and Zibo Zhuang

Biological invasion in a predator–prey model with a free boundary

In this paper we study a predator–prey system with free boundary in a one-dimensional environment. The predator v is the invader which exists initially in a sub-interval ...

Authors: Yunfeng Liu, Zhiming Guo, Mohammad El Smaily and Lin Wang

A general decay result for a semilinear heat equation with past and finite history memories

In this paper, we consider the initial-boundary value problem of the following semilinear heat equation with past and finite history memories:

Authors: Rui Yang and Zhong Bo Fang

Nonexistence and existence of nontrivial solutions for Klein–Gordon–Maxwell systems with competing nonlinearities

Authors: Chongqing Wei and Anran Li

Regularity criteria for the two-and-half-dimensional magnetic Bénard system with partial dissipation, magnetic diffusion, and thermal diffusivity

Authors: Liangliang Ma and Lei Zhang

On the \(\mathcal{PC}\)-mild solutions of abstract fractional evolution equations with non-instantaneous impulses via the measure of noncompactness

In this paper, we deal with the existence results for mild solutions of abstract fractional evolution equations with non-instantaneous impulses on an unbounded interval. We also establish the existence of

Authors: R. Saadati, E. Pourhadi and B. Samet

A quasi-reversibility regularization method for a Cauchy problem of the modified Helmholtz-type equation

The Cauchy problem of the modified Helmholtz-type equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Thus the regularization methods are required to recov...

Authors: Hong Yang and Yanqi Yang

Unique solvability and stability of the time domain electromagnetic scattering problem with a locally perturbed perfectly conducting plate

In this paper, we investigate the unique solvability and stability of the time domain electromagnetic scattering problem with a kind of unbounded scatterer, that is, a locally perturbed perfectly electrical co...

Authors: Minfu Zhang, Fuming Ma and Bo Chen

Infinitely many solutions for nonlinear Klein–Gordon–Maxwell system with general nonlinearity

Authors: Wang Hu and Shulin Liang

Study on variable coefficients singular differential equation via constant coefficients differential equation

Authors: Shaowen Yao and Jie Liu

Suction/injection effects on an unsteady MHD Casson thin film flow with slip and uniform thickness over a stretching sheet along variable flow properties

In this investigation the attention is given to a mathematical model of the non-Newtonian Casson liquid over an unsteady stretching sheet under the combined effects of different natural parameters with heat tr...

Authors: Sajid Rehman, M. Idrees, Rehan Ali Shah and Zeeshan Khan

Least energy sign-changing solutions for the fractional Schrödinger–Poisson systems in \(\mathbb{R}^{3}\)

Authors: Da-Bin Wang, Yu-Mei Ma and Wen Guan

Solutions to a phase-field model of sea ice growth

We shall apply the phase-field method to investigate the dynamics of sea ice growth. The model consists of two parabolic equations. The existence and uniqueness of weak solutions to an initial-boundary value p...

Authors: Yangxin Tang

Topological sensitivity analysis of a time-dependent nonlinear problem

We are interested in the optimization of the pipe shape allowing minimization of the dissipated energy in time-dependent Navier–Stokes Darcy flow. The used technique is based on the topological gradient method...

Authors: Mohamed Abdelwahed, Azhar Al Salem, Nejmeddine Chorfi and Maatoug Hassine

Existence and uniqueness of positive solutions for fractional differential equations

By some new integral inequalities of Henry–Gronwall type, we investigate the existence and uniqueness of positive solutions for fractional differential equations.

Authors: Tao Zhu

Uniqueness and stability of solutions without the boundary condition

A parabolic equation related to the p-Laplacian is considered. If the equation is degenerate on the boundary, then demonstrating the regularity on the boundary is difficult, the trace on the boundary cannot be de...

Authors: Huashui Zhan

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

The rotational motion of fractional Maxwell fluids in an infinite circular cylinder that applies a time-dependent but not oscillating couple stress to the fluid is investigated using the integral transform tec...

Authors: Naeem Sadiq, Muhammd Imran, Constantin Fetecau and Najma Ahmed

Global existence and blow-up of solution for the semilinear wave equation with interior and boundary source terms

This paper is concerned with semilinear wave equations with nonlinear interior and boundary sources and subject to a nonlinear dynamical boundary condition. By using the potential well method combined with a s...

Authors: Hongwei Zhang, Wenxiu Zhang and Qingying Hu

Solvability and coerciveness of multi-point Sturm–Liouville problems with abstract linear functionals

In this paper, we consider a Sturm–Liouville problem with finite discontinuous points inside an interval and with abstract linear functionals in the boundary and transmission conditions. For such a problem, th...

Authors: Yulin Bai, Wanyi Wang and Kun Li

Local existence of the generalized solution for three-dimensional compressible viscous flow of micropolar fluid with cylindrical symmetry

In this work, the three-dimensional model for the compressible micropolar fluid flow is considered, whereby it is assumed that the fluid is viscous, perfect, and heat conducting. The flow between two coaxial t...

Authors: Ivan Dražić and Nermina Mujaković

Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level

In this paper, we study the initial boundary value problem for a Petrovsky type equation with a memory term, nonlinear weak damping, and a superlinear source:

Authors: Lishan Liu, Fenglong Sun and Yonghong Wu

Difference numerical solutions for time-space fractional advection diffusion equation

In this paper, a time-space fractional advection diffusion equation is considered for the natural extension of the convection diffusion equation. An explicit difference scheme and an implicit difference scheme...

Authors: Fangfang Zhang, Xiaoyang Gao and Zhaokun Xie

Some results on the eigenvalue problem for a fractional elliptic equation

This paper deals with the eigenvalue problem for a fractional variable coefficients elliptic equation defined on a bounded domain. Compared to the previous work, we prove a quite different variational formulat...

Authors: Yujuan Tian

Peristaltic motion of MHD nanofluid in an asymmetric micro-channel with Joule heating, wall flexibility and different zeta potential

A mathematical scrutiny is introduced for the flow of magneto-hydrodynamic nanofluid through an asymmetric microfluidic channel under an applied axial electric field. The impacts of wall flexibility, Joule hea...

Authors: S. Noreen, S. Waheed and A. Hussanan