Articles

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This article has been retracted.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

A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the ne...

Authors: Gang Dong and Boying Wu

Mathematical analysis of nonlinear integral boundary value problem of proportional delay implicit fractional differential equations with impulsive conditions

The current study is devoted to deriving some results about existence and stability analysis for a nonlinear problem of implicit fractional differential equations (FODEs) with impulsive and integral boundary c...

Authors: Arshad Ali, Kamal Shah, Thabet Abdeljawad, Ibrahim Mahariq and Mostafa Rashdan

Infinitely many homoclinic solutions for sublinear and nonperiodic Schrödinger lattice systems

By using variational methods we obtain infinitely many nontrivial solutions for a class of nonperiodic Schrödinger lattice systems, where the nonlinearities are sublinear at both zero and infinity.

Authors: Guanwei Chen and Jijiang Sun

Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

In this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the he...

Authors: Liming Xiao and Mingkun Li

Steady state for a predator–prey cross-diffusion system with the Beddington–DeAngelis and Tanner functional response

The main goal of this paper is investigating the existence of nonconstant positive steady states of a linear prey–predator cross-diffusion system with Beddington–DeAngelis and Tanner functional response. An an...

Authors: Demou Luo

Hopf bifurcation in a delayed reaction–diffusion–advection equation with ideal free dispersal

In this paper, we investigate a delay reaction–diffusion–advection model with ideal free dispersal. The stability of positive steady-state solutions and the existence of the associated Hopf bifurcation are obt...

Authors: Yunfeng Liu and Yuanxian Hui

\(L^{\infty }\) decay estimates of solutions of nonlinear parabolic equation

Authors: Hui Wang and Caisheng Chen

How far does logistic dampening influence the global solvability of a high-dimensional chemotaxis system?

Authors: Ke Jiang and Yongjie Han

The exterior Dirichlet problems of Monge–Ampère equations in dimension two

Authors: Limei Dai

The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)

In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain t...

Authors: Bingyu Kou, Tianqing An and Zeyan Wang

A novel method in determining a layered periodic structure

This paper is concerned with the inverse scattering of time-harmonic waves by a penetrable structure. By applying the integral equation method, we establish the uniform ...

Authors: Yanli Cui, Xiliang Li and Fenglong Qu

Nonlocal boundary value problems for integro-differential Langevin equation via the generalized Caputo proportional fractional derivative

Results reported in this paper study the existence and stability of a class of implicit generalized proportional fractional integro-differential Langevin equations with nonlocal fractional integral conditions....

Authors: Bounmy Khaminsou, Chatthai Thaiprayoon, Jehad Alzabut and Weerawat Sudsutad

On global dynamics of 2D convective Cahn–Hilliard equation

Authors: Xiaopeng Zhao

The mixed problem in the theory of strain gradient thermoelasticity approached with the Lagrange identity

In our paper we address the thermoelasticity theory of the strain gradient. First, we define the mixed problem with initial and boundary data in this context. Then, with the help of an identity of Lagrange typ...

Authors: Marin Marin, Sorin Vlase and Ioan Tuns

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