Articles

Global existence and exponential stability of coupled Lamé system with distributed delay and source term without memory term

In this paper, we prove the global existence and exponential energy decay results of a coupled Lamé system with distributed time delay, nonlinear source term, and without memory term by using the Faedo–Galerki...

Authors: Salah Boulaaras and Nadjat Doudi

General decay and blow-up of solutions for a nonlinear wave equation with memory and fractional boundary damping terms

The paper studies the global existence and general decay of solutions using Lyapunov functional for a nonlinear wave equation, taking into account the fractional derivative boundary condition and memory term. ...

Authors: Salah Boulaaras, Fares Kamache, Youcef Bouizem and Rafik Guefaifia

On a new structure of the pantograph inclusion problem in the Caputo conformable setting

In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the...

Authors: Sabri T. M. Thabet, Sina Etemad and Shahram Rezapour

New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumpti...

Authors: Mohammad M. Al-Gharabli, Adel M. Al-Mahdi and Salim A. Messaoudi

Construction of invariant solutions and conservation laws to the \((2+1)\)-dimensional integrable coupling of the KdV equation

Authors: Ben Gao and Qinglian Yin

On resonant mixed Caputo fractional differential equations

The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional deriv...

Authors: Assia Guezane-Lakoud and Adem Kılıçman

Resolution and implementation of the nonstationary vorticity velocity pressure formulation of the Navier–Stokes equations

This paper deals with the iterative algorithm and the implementation of the spectral discretization of time-dependent Navier–Stokes equations in dimensions two and three. We present a variational formulation, ...

Authors: Mohamed Abdelwahed, Ebtisam Alharbi, Nejmeddine Chorfi and Henda Ouertani

Normalized solutions for a coupled fractional Schrödinger system in low dimensions

Authors: Meng Li, Jinchun He, Haoyuan Xu and Meihua Yang

Well-posedness and behaviors of solutions to an integrable evolution equation

This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and un...

Authors: Sen Ming, Shaoyong Lai and Yeqin Su

Existence of positive periodic solutions for super-linear neutral Liénard equation with a singularity of attractive type

Authors: Yu Zhu

Existence of solutions for functional boundary value problems at resonance on the half-line

By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functi...

Authors: Bingzhi Sun and Weihua Jiang

Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control

In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theo...

Authors: Shu Song, Lingling Zhang, Bibo Zhou and Nan Zhang

An efficient meshless radial point collocation method for nonlinear p-Laplacian equation

This paper considered the spectral meshless radial point interpolation (SMRPI) method to unravel for the nonlinear p-Laplacian equation with mixed Dirichlet and Neumann boundary conditions. Through this assessmen...

Authors: Samaneh Soradi-Zeid, Mehdi Mesrizadeh and Thabet Abdeljawad

Retraction Note: A note on the boundary behavior for a modified Green function in the upper-half space

This article has been retracted. Please see the retraction notice for more detail: https://​doi.​org/​10.​1186/​s13661-015-0363-z.

Authors: Yulian Zhang and Valery Piskarev

Multiplicity results for sublinear elliptic equations with sign-changing potential and general nonlinearity

Authors: Wei He and Qingfang Wu

Low Mach number limit for the compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition

In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain. The main idea is to deri...

Authors: Dandan Ren, Yunting Ding and Xinfeng Liang

Existence of positive solutions for singular Dirichlet boundary value problems with impulse and derivative dependence

In this paper, we present a theorem for some impulsive boundary problems with derivative dependence by the upper and lower solutions method. Using the theorem obtained, we consider the existence of positive so...

Authors: Fengfei Jin and Baoqiang Yan

The applications of Sobolev inequalities in proving the existence of solution of the quasilinear parabolic equation

The aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the qu...

Authors: Yuanfei Li, Lianhong Guo and Peng Zeng

Existence results for first derivative dependent ϕ-Laplacian boundary value problems

Authors: Imran Talib and Thabet Abdeljawad

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