Articles

On the fractional partial integro-differential equations of mixed type with non-instantaneous impulses

In this paper, we consider the initial boundary value problem for a class of nonlinear fractional partial integro-differential equations of mixed type with non-instantaneous impulses in Banach spaces. Sufficie...

Authors: Bo Zhu, Baoyan Han, Lishan Liu and Wenguang Yu

Nonlinear nonhomogeneous Dirichlet problems with singular and convection terms

We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturba...

Authors: Nikolaos S. Papageorgiou and Youpei Zhang

Spectral discretization of time-dependent vorticity–velocity–pressure formulation of the Navier–Stokes equations

In this work, we propose a nonstationary Navier–Stokes problem equipped with an unusual boundary condition. The time discretization of such a problem is based on the backward Euler’s scheme. However, the varia...

Authors: Mohamed Abdelwahed and Nejmeddine Chorfi

Blow-up criterion for the density dependent inviscid Boussinesq equations

Authors: Li Li and Yanping Zhou

Multiplicity of solutions for a class of fractional \(p(x,\cdot )\)-Kirchhoff-type problems without the Ambrosetti–Rabinowitz condition

Authors: M. K. Hamdani, J. Zuo, N. T. Chung and D. D. Repovš

Existence of a mountain pass solution for a nonlocal fractional \((p, q)\)-Laplacian problem

Authors: F. Behboudi, A. Razani and M. Oveisiha

Ground states for infinite lattices with nearest neighbor interaction

Sun and Ma (J. Differ. Equ. 255:2534–2563, 2013) proved the existence of a nonzero T-periodic solution for a class of one-dimensional lattice dynamical systems,

Authors: Peng Chen, Die Hu and Yuanyuan Zhang

Higher integrability for obstacle problem related to the singular porous medium equation

In this paper we study the self-improving property of the obstacle problem related to the singular porous medium equation by using the method developed by Gianazza and Schwarzacher (J. Funct. Anal. 277(12):1–57,

Authors: Qifan Li

On locally superquadratic Hamiltonian systems with periodic potential

Authors: Yiwei Ye

Concentrated solutions for a critical nonlocal problem

In this paper, we deal with a class of fractional critical problems. Under some suitable assumptions, we derive the existence of a positive solution concentrating at the critical point of the Robin function by...

Authors: Qingfang Wang

The existence of nontrivial solution of a class of Schrödinger–Bopp–Podolsky system with critical growth

Authors: Jie Yang, Haibo Chen and Senli Liu

Weak and strong singularities problems to Liénard equation

Authors: Yun Xin and Guixin Hu

Infinitely many positive solutions for a double phase problem

This paper is concerned with the existence of infinitely many positive solutions to a class of double phase problem. By variational methods and the theory of the Musielak–Orlicz–Sobolev space, we establish the...

Authors: Bei-Lei Zhang, Bin Ge and Gang-Ling Hou

On decay and blow-up of solutions for a nonlinear Petrovsky system with conical degeneration

Authors: Jiali Yu, Yadong Shang and Huafei Di

Existence of solutions for tripled system of fractional differential equations involving cyclic permutation boundary conditions

In this paper, we introduce and study a tripled system of three associated fractional differential equations. Prior to proceeding to the main results, the proposed system is converted into an equivalent integr...

Authors: Mohammed M. Matar, Iman Abo Amra and Jehad Alzabut

Boundary shape function method for nonlinear BVP, automatically satisfying prescribed multipoint boundary conditions

It is difficult to exactly and automatically satisfy nonseparable multipoint boundary conditions by numerical methods. With this in mind, we develop a novel algorithm to find solution for a second-order nonlin...

Authors: Chein-Shan Liu and Chih-Wen Chang

Qualitative analysis of nonlinear coupled pantograph differential equations of fractional order with integral boundary conditions

In this research article, we develop a qualitative analysis to a class of nonlinear coupled system of fractional delay differential equations (FDDEs). Under the integral boundary conditions, existence and uniq...

Authors: Hussam Alrabaiah, Israr Ahmad, Kamal Shah and Ghaus Ur Rahman

Well-posedness of the solution of the fractional semilinear pseudo-parabolic equation

This article concerns the Cauchy problem for the fractional semilinear pseudo-parabolic equation. Through the Green’s function method, we prove the pointwise convergence rate of the solution. Furthermore, usin...

Authors: Jiazhuo Cheng and Shaomei Fang

On the numerical solutions of two-dimensional scattering problems for an open arc

For the scattering problems of acoustic wave for an open arc in two dimensions, we give a uniqueness and existence analysis via the single layer potential approach leading to a system of integral equations tha...

Authors: Hu Li, Jin Huang and Guang Zeng

On a system of fractional q-differential inclusions via sum of two multi-term functions on a time scale

Nowadays most researchers have been focused on fractional calculus because it has been proved that fractional derivatives could describe most phenomena better than usual derivations. Numerical parts of fractio...

Authors: Mohammad Esmael Samei and Shahram Rezapour

Existence result for a Kirchhoff elliptic system with variable parameters and additive right-hand side via sub- and supersolution method

The paper deals with the study of the existence result for a Kirchhoff elliptic system with additive right-hand side and variable parameters by using the sub-/supersolution method. Our study is a natural exten...

Authors: Mohamed Haiour, Salah Boulaaras, Youcef Bouizem and Rafik Guefaifia

Ground state and nodal solutions for critical Kirchhoff–Schrödinger–Poisson systems with an asymptotically 3-linear growth nonlinearity

In this paper, we consider the existence of a least energy nodal solution and a ground state solution, energy doubling property and asymptotic behavior of solutions of the following critical problem:

Authors: Chungen Liu and Hua-Bo Zhang

Hopf bifurcation analysis of nonlinear HIV infection model and the effect of delayed immune response with drug therapies

A mathematical model of HIV infection with the combination of drug therapy including cytotoxic T-lymphocyte (CTL) and the antibody immune response is examined. The threshold value represented as the basic repr...

Authors: V. Geetha and S. Balamuralitharan

On the existence of three solutions of Dirichlet fractional systems involving the p-Laplacian with Lipschitz nonlinearity

Authors: Rafik Guefaifia, Salah Boulaaras and Fares Kamache

Existence and multiplicity of solutions for nonlocal fourth-order elliptic equations with combined nonlinearities

Authors: Ru Yuanfang and An Yukun

A note on singular two-dimensional fractional coupled Burgers’ equation and triple Laplace Adomian decomposition method

The present article focuses on how to find the exact solutions of the time-fractional regular and singular coupled Burgers’ equations by applying a new method that is called triple Laplace and Adomian decompos...

Authors: Hassan Eltayeb and Imed Bachar

Properties of solutions to fractional p-subLaplace equations on the Heisenberg group

The aim of this paper is to study properties of solutions to the fractional p-subLaplace equations on the Heisenberg group. Based on the maximum principles and the generalization of the direct method of moving pl...

Authors: Xinjing Wang and Guangwei Du

Retraction Note: Notes on the result of solutions of the equilibrium equations

The Editor-in-Chief has retracted this article [1] because the results are invalid. The article also shows evidence of authorship manipulation. Additionally, Universidad de Talca have confirmed that Ben Rodrig...

Authors: Gaiping He, Lihong Wang and Ben Rodrigo

Retraction Note: Normal families of solutions for modified equilibrium equations and their applications

The Editors-in-Chief have retracted this article [1] because its results are invalid. It also shows considerable overlap with an article by Lu and Sun [2] that was simultaneously under consideration. Additiona...

Authors: Yili Tan, Weiyong Ding, Yourong Wang and Zongjing Jiang

Existence of ground state for fractional Kirchhoff equation with \(L^{2}\) critical exponents

Authors: Yaling Han and Yimin Zhang

Nonlinear eigenvalue problems for nonhomogeneous Leray–Lions operators

This paper deals with the mathematical analysis of a class of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator. We are concerned both with the coercive and the noncoercive (and no...

Authors: Mohamed Abdelwahed and Nejmeddine Chorfi

Local solvability and stability of the inverse problem for the non-self-adjoint Sturm–Liouville operator

We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight n...

Authors: Natalia P. Bondarenko

Existence of ground state solutions for quasilinear Schrödinger equations with general Choquard type nonlinearity

Authors: Yu-bo He, Jue-liang Zhou and Xiao-yan Lin

Existence and multiplicity of solutions for Schrödinger–Kirchhoff type problems involving the fractional \(p(\cdot )\)-Laplacian in \(\mathbb{R}^{N}\)

Authors: In Hyoun Kim, Yun-Ho Kim and Kisoeb Park

Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion

We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brown...

Authors: Hamdy M. Ahmed, Mahmoud M. El-Borai, A. S. Okb El Bab and M. Elsaid Ramadan

Controllability of fractional evolution systems of Sobolev type via resolvent operators

Authors: He Yang and Yanjie Zhao

Multiplicity results involving p-biharmonic Kirchhoff-type problems

Authors: Ramzi Alsaedi

Existence–uniqueness and monotone iteration of positive solutions to nonlinear tempered fractional differential equation with p-Laplacian operator

Authors: Bibo Zhou, Lingling Zhang, Gaofeng Xing and Nan Zhang

Global attractors for Kirchhoff wave equation with nonlinear damping and memory

In this paper, we prove that the existence of global attractors for a Kirchhoff wave equation with nonlinear damping and memory.

Authors: Suli Zhang, Jianwen Zhang and Haiyan Wang

The initial-boundary value problem for a class of third order pseudoparabolic equations

In this paper, a priori estimate for a linear third pseudoparabolic operator with bound is established, and applying the above result, the existence and uniqueness theorem of solutions for a class of nonlinear...

Authors: Yanqing Feng, Limin Guo and Zhongying Wang

Existence of solution for a resonant p-Laplacian second-order m-point boundary value problem on the half-line with two dimensional kernel

The existence of a solution for a second-order p-Laplacian boundary value problem at resonance with two dimensional kernel will be considered in this paper. A semi-projector, the Ge and Ren extension of Mawhin...

Authors: O. F. Imaga and S. A. Iyase

Existence and uniqueness of finite beam deflection on nonlinear non-uniform elastic foundation with arbitrary well-posed boundary condition

For arbitrary two-point boundary condition, which makes the corresponding linear uniform problem well-posed, we obtain an existence and uniqueness result for the boundary value problem of finite beam deflectio...

Authors: Sung Woo Choi

Existence of nontrivial solutions for fractional Schrödinger equations with electromagnetic fields and critical or supercritical nonlinearity

Authors: Quanqing Li, Kaimin Teng, Wenbo Wang and Jian Zhang

Existence of least energy nodal solution for Kirchhoff–Schrödinger–Poisson system with potential vanishing

Authors: Jin-Long Zhang and Da-Bin Wang

Boundary value conditions for linear differential equations with power degenerations

Authors: Aigerim Kalybay

Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth

Authors: Jing Zhang, Lifeng Guo and Miaomiao Yang

Infinitely many positive solutions for a nonlocal problem with competing potentials

The present paper deals with a class of nonlocal problems. Under some suitable assumptions on the decay rate of the coefficients, we derive the existence of infinitely many positive solutions to the problem by...

Authors: Jing Yang

The global dynamics for an age-structured SLIS model with the delay

This paper deals with the global dynamics for a SLIS epidemic model with infection age. In our model, we also consider the time delay in the progression from the latent individuals to becoming infectious indiv...

Authors: Hongwu Tan, Xin Yang and Hui Cao

Existence of infinitely many solutions for a p-Kirchhoff problem in RN

Authors: Zonghu Xiu, Jing Zhao and Jianyi Chen

New analytical method based on dynamic response of planar mechanical elastic systems

An important stage in an analysis of a multibody system (MBS) with elastic elements by the finite element method is the assembly of the equations of motion for the whole system. This assembly, which seems like...

Authors: Maria Luminiţa Scutaru, Sorin Vlase, Marin Marin and Arina Modrea