Articles

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

Ground states for planar axially Schrödinger–Newton system with an exponential critical growth

Authors: Wenbo Wang, Quanqing Li and Yongkun Li

Existence of a random attractor for non-autonomous stochastic plate equations with additive noise and nonlinear damping on \(\mathbb{R}^{n}\)

Based on the abstract theory of pullback attractors of non-autonomous non-compact dynamical systems by differential equations with both dependent-time deterministic and stochastic forcing terms, introduced by ...

Authors: Xiaobin Yao

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

Obstacle detection in fluid flow using asymptotic analysis technique

We consider the geometric inverse problem of determining an immersed obstacle in a two-dimensional non-stationary Stokes fluid flow. We use the topological gradient method to solve this problem. The unknown ob...

Authors: Rakia Malek, Mohamed Abdelwahed, Nejmeddine Chorfi and Maatoug Hassine

Multiplicity of positive solutions for Hadamard fractional differential equations with p-Laplacian operator

In this paper, we investigate the multiplicity results of some positive solutions for a system of Hadamard fractional differential equations with parameters and p-Laplacian operator subject to three-point boundar...

Authors: Sabbavarapu Nageswara Rao, Manoj Singh and M. Zico Meetei

Stieltjes differential systems with nonmonotonic derivators

In this work we study Stieltjes differential systems of which the derivators are allowed to change sign. This leads to the definition of the notion of a function of controlled variation, a characterization of pre...

Authors: Marlène Frigon and F. Adrián F. Tojo

Existence of positive solutions for nonlocal problems with indefinite nonlinearity

Authors: Xiaotao Qian and Wen Chao

On the existence of solutions for a multi-singular pointwise defined fractional q-integro-differential equation

By using the Caputo type and the Riemann–Liouville type fractional q-derivative, we investigate the existence of solutions for a multi-term pointwise defined fractional q-integro-differential equation with some b...

Authors: Shahram Rezapour and Mohammad Esmael Samei

Global existence and blow-up analysis for parabolic equations with nonlocal source and nonlinear boundary conditions

Authors: Wei Kou and Juntang Ding

Retraction Note: An augmented Riesz decomposition method for sharp estimates of certain boundary value problem

The Editors-in-Chief have retracted this article [1] because it shows evidence of peer review manipulation and authorship manipulation. In addition, the identity of the corresponding author could not be verifi...

Authors: Jiaofeng Wang, Bin Huang and Nanjundan Yamini

Global weak conservative solutions of the μ-Camassa–Holm equation

In this paper we consider global weak conservative solutions of a μ-Camassa–Holm equation. By employing a technique of change of variables on the Lagrangian variable, we successfully construct global weak conserv...

Authors: Xijun Deng and Aiyong Chen

Certain new dynamic nonlinear inequalities in two independent variables and applications

Several inequalities were proved in 2018 by Boudeliou, in 2015 by Abdeldain and El-Deeb and in 1998 by Pachpatte. It is our aim in this paper to generalize these inequalities to time scales. Beside that, we al...

Authors: A. A. El-Deeb and Zareen A. Khan

Time periodic Navier–Stokes equations in a thin tube structure

The time periodic Navier–Stokes equations are considered in the three-dimensional and two-dimensional settings with Dirichlet boundary conditions in thin tube structures. These structures are finite union of t...

Authors: R. Juodagalvytė, G. Panasenko and K. Pileckas

Two nontrivial solutions for a nonhomogeneous fractional Schrödinger–Poisson equation in \(\mathbb{R}^{3}\)

Authors: Ruiting Jiang and Chengbo Zhai

Multiple positive solutions for nonlinear high-order Riemann–Liouville fractional differential equations boundary value problems with p-Laplacian operator

In this paper, we study the existence of multiple positive solutions for boundary value problems of high-order Riemann–Liouville fractional differential equations involving the p-Laplacian operator. Not only new ...

Authors: Bibo Zhou, Lingling Zhang, Emmanuel Addai and Nan Zhang

Retraction Note: Some new results on the boundary behaviors of harmonic functions with integral boundary conditions

The Editors-in-Chief have retracted this article [1] because it significantly overlaps with an article by different authors [2] that was simultaneously under consideration at another journal. The article also ...

Authors: Xiaozhen Xie and Costanza T. Viouonu

Ground state sign-changing solutions for a class of double-phase problem in bounded domains

Authors: Gangling Hou, Bin Ge, Beilei Zhang and Liyan Wang

Existence of solutions for integral boundary value problems of mixed fractional differential equations under resonance

Authors: Shiying Song and Yujun Cui

Ground states for a coupled Schrödinger system with general nonlinearities

We study a coupled Schrödinger system with general nonlinearities. By using variational methods, we prove the existence and asymptotic behaviour of ground state solution for the system with periodic couplings....

Authors: Xueliang Duan, Gongming Wei and Haitao Yang

The existence of solutions for perturbed fractional differential equations with impulses via Morse theory

In the present paper, the existence of nontrivial solutions of impulsive fractional differential equations with Dirichlet boundary conditions is studied. We apply Morse theory coupled with local linking argume...

Authors: Peiluan Li, Liang Xu, Hui Wang and Yumeng Wang

An exponential spline approximation for fractional Bagley–Torvik equation

In this paper, we approximate the solution of fractional Bagley–Torvik equation by using the exponential spline function and the shifted Grünwald difference operator. The proposed methods reduce to the system ...

Authors: Homan Emadifar and Reza Jalilian

On weak solutions to a generalized Camassa–Holm equation with solitary wave

A generalized Camassa–Holm equation proposed by Novikov is considered. The existence and uniqueness of a positive weak solution for the equation is established by using a classical method.

Authors: Yunxi Guo

Liouville-type theorem for Kirchhoff equations involving Grushin operators

Authors: Yunfeng Wei, Caisheng Chen and Hongwei Yang

Retraction Note: Growth properties of Green-Sch potentials at infinity

The Editors-in-Chief have retracted this article [1] because it shows evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Stockholms Universitet h...

Authors: Tao Zhao and Alexander Yamada Jr.

Retraction Note: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

The Editors-in-Chief have retracted this article [1] because it shows evidence of peer review manipulation. In addition, it overlaps significantly with an article by Sun et al. [2] that was simultaneously unde...

Authors: Jianjie Wang, Ali Mai and Hong Wang

Retraction Note: A new application of boundary integral behaviors of harmonic functions to the least harmonic majorant

The Editors-in-Chief have retracted this article [1] because of overlap with articles from different authors that were simultaneously under consideration with another journal [2, 3]. Additionally, this article...

Authors: Minghua Han, Jianguo Sun and Gaoying Xue

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

This paper is concerned with the global existence of solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation. Firstly, based on the Schrödinger approximation technique and t...

Authors: Zhen Liu

The existence, uniqueness and asymptotic estimates of solutions for third-order full nonlinear singularly perturbed vector boundary value problems

In this paper, we discuss third-order full nonlinear singularly perturbed vector boundary value problems. We first present the existence of solutions for the nonlinear vector boundary value problems without pe...

Authors: Xiaojie Lin, Jiang Liu and Can Wang

Head-on collision between capillary–gravity solitary waves

The present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is su...

Authors: Marin Marin and M. M. Bhatti

On solutions of a class of three-point fractional boundary value problems

Authors: Zhanbing Bai, Yu Cheng and Sujing Sun

Local existence and uniqueness of increasing positive solutions for non-singular and singular beam equation with a parameter

This paper is concerned with a class of beam equations with a parameter. By using the fixed point theorems of mixed monotone operator and the properties of cone, we study the non-singular and singular case, re...

Authors: Hui Wang and Lingling Zhang

Linear difference operator with multiple variable parameters and applications to second-order differential equations

Authors: Feifan Li, Zhonghua Bi, Shaowen Yao and Yun Xin

Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients

Authors: Jinghong Liu and Qiding Zhu

Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inher...

Authors: Maozhu Zhang, Kun Li and Hongxiang Song

Existence of ground state solutions for an asymptotically 2-linear fractional Schrödinger–Poisson system

Authors: Dandan Yang and Chuanzhi Bai

Multiple homoclinic solutions for p-Laplacian Hamiltonian systems with concave–convex nonlinearities

Authors: Lili Wan

Stability analysis and prevention strategies of tobacco smoking model

This research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the formulation of the model containing snuffing class is pre...

Authors: Ebraheem Alzahrani and Anwar Zeb