Articles

Fixed point theorems for a class of nonlinear sum-type operators and application in a fractional differential equation

Authors: Hui Wang, Lingling Zhang and Xiaoqiang Wang

A global nonexistence of solutions for a quasilinear viscoelastic wave equation with acoustic boundary conditions

In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g, the function Φ, ...

Authors: Yong Han Kang, Jong Yeoul Park and Daewook Kim

A diffusive stage-structured model with a free boundary

In this paper we mainly consider a free boundary problem for a single-species model with stage structure in a radially symmetric setting. In our model, the individuals of a new or invasive species are classifi...

Authors: Jingfu Zhao, Changming Song and Hongtao Zhang

Existence of a regular solution for 1D Green–Naghdi equations with surface tension at a large time instant

In this paper the model 1D-GNσ is considered, which concerns the 1D Green–Naghdi equations with non-flat bottom and under the influence of surface tension, to be widely used in coastal oceanography to describe th...

Authors: Mohammad Haidar, Toufic El Arwadi and Samer Israwi

Positive solutions of conformable fractional differential equations with integral boundary conditions

Authors: Wenyong Zhong and Lanfang Wang

Schrödinger-type identity for Schrödinger free boundary problems

Authors: Xingjian Zhang, Duo Liu, Zining Yan, Guodong Zhao and Ye Yuan

Existence of solutions for several higher-order Hadamard-type fractional differential equations with integral boundary conditions on infinite interval

In this paper, we investigate the existence of solutions for several higher-order integral boundary value problems of Hadamard-type fractional differential equations on an infinite interval by using the monoto...

Authors: Wei Zhang and Wenbin Liu

New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition

In this paper, we introduce a new mixed condition to obtain a new compact embedding theorem. Under this theorem, we study the existence and multiplicity of nontrivial homoclinic solutions for a class of second...

Authors: Xuefeng Li and Jin Jia

Bifurcation results for the critical Choquard problem involving fractional p-Laplacian operator

By using an abstract critical point theorem based on a pseudo-index related to the cohomological index, we prove the bifurcation results for the critical Choquard problems involving fractional p-Laplacian operato...

Authors: Yuling Wang and Yang Yang

Hölder continuity of weak solution to a nonlinear problem with non-standard growth conditions

We study the Hölder continuity of weak solution u to an equation arising in the stationary motion of electrorheological fluids. To this end, we first obtain higher integrability of Du in our case by establishing ...

Authors: Zhong Tan, Jianfeng Zhou and Wenxuan Zheng

On a class of stationary loops on \(\mathbf{SO}(n)\) and the existence of multiple twisting solutions to a nonlinear elliptic system subject to a hard incompressibility constraint

Authors: George Morrison and Ali Taheri

Adaptive stabilized finite volume method and convergence analysis for the Oseen equations

In this paper, based on the pressure project method, we consider an adaptive stabilized finite volume method for the Oseen equations with the lowest equal order finite element pair. Firstly, we develop the dis...

Authors: Junxiang Lu and Tong Zhang

Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses

In this paper, we study periodic boundary value problems of fractional semilinear integro-differential equations with non-instantaneous impulses in Banach spaces. By the measure of noncompactness, the theory of β

Authors: Bo Zhu and Lishan Liu

Multiplicity for fractional differential equations with p-Laplacian

This paper investigates the existence of positive solution for a boundary value problem of fractional differential equations with p-Laplacian operator. Our analysis relies on the research of properties of the cor...

Authors: Yuansheng Tian, Yongfang Wei and Sujing Sun

Heat transfer over a steady stretching surface in the presence of suction

The purpose of this paper is to present the Cattaneo–Christov heat flux model for Maxwell fluid past a stretching surface where the presence of suction/injection is taken into account. The governing system of ...

Authors: Zailan Siri, Nor Artisham Che Ghani and Ruhaila Md. Kasmani

Existence of solutions for the fractional Kirchhoff equations with sign-changing potential

Authors: Guoqing Chai and Weiming Liu

On the well-posedness of generalized Darcy–Forchheimer equation

Under the necessary compatibility condition and some mild regularity assumptions on the interior and the boundary data, we prove the existence, uniqueness, and stability of solution in ...

Authors: Johnson D. Audu, Faisal A. Fairag and Salim A. Messaoudi

Existence and multiplicity of solutions for a p-Kirchhoff equation on \({\mathbb {R}}^{N}\)

Authors: Jincheng Huang

On the stability of Rayleigh–Taylor problem for stratified rotating viscoelastic fluids

We investigate the stability of Rayleigh–Taylor (RT) problem of the stratified incompressible viscoelastic fluids under the rotation and the gravity in a horizontal periodic domain, in which the rotation axis ...

Authors: Yi Jiang, Xianjuan Li and Youyi Zhao

Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity

Authors: Lijun Yan and Zuodong Yang

Classical and weak solutions of the partial differential equations associated with a class of two-point boundary value problems

This paper is concerned with a kind of first-order quasilinear parabolic partial differential equations associated with a class of ordinary differential equations with two-point boundary value problems. We pro...

Authors: Ning Ma and Zhen Wu

Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces

In this paper, we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence and uniqueness of periodic solutions for a class of fractional differential equations ...

Authors: Yonghong Ding and Yongxiang Li

Well-posedness of a ratio-dependent Lotka–Volterra system with feedback control

The main purpose of this article is to consider a Lotka–Volterra predator–prey system with ratio-dependent functional responses and feedback controls. By using a comparison theorem and constructing a suitable ...

Authors: Changyou Wang, Yuqian Zhou, Yonghong Li and Rui Li

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption terms subject to null Dirichlet boundary condition. Based on a modified differential inequal...

Authors: Yunde Shen and Zhong Bo Fang

Positive solutions for a class of fractional infinite-point boundary value problems

In this paper, we consider a class of fractional differential equations with infinite-point boundary value conditions. Under some conditions concerning the spectral radius with respect to the relevant linear o...

Authors: Yongqing Wang and Lishan Liu

On positive periodic solutions of second order singular equations

Using the fixed point theorem, we study the existence and multiplicity of positive periodic solutions for the second order differential equations

Authors: Yunhai Wang and Yuanfang Ru

Weighted Lorentz estimates for nonlinear elliptic obstacle problems with partially regular nonlinearities

A global estimate in the framework of weighted Lorentz spaces is reached for the gradient of weak solution to a class of nonlinear elliptic obstacle problems with partially regular nonlinearities in a bounded ...

Authors: Hong Tian, Shenzhou Zheng and Xiuying Kang

The existence of affine-periodic solutions for nonlinear impulsive differential equations

In this paper, we study the existence of affine-periodic solutions of nonlinear impulsive differential equations. The affine-periodic solutions have the form ...

Authors: Shuai Wang

On a generalized relaxed Saint–Venant principle

The goal of this paper is to obtain an extension of the relaxed Saint–Venant principle in order to cover the thermoelasticity of dipolar porous bodies.

Authors: Marin Marin, Ravi P. Agarwal and Dumitru Baleanu

Dynamical analysis of a competition and cooperation system with multiple delays

This paper is concerned with a competition and cooperation system with multiple constant delays relating to economic enterprise. The stability of the unique positive equilibrium is investigated and the existen...

Authors: Xin Zhang, Zizhen Zhang and Matthew J. Wade

Existence of the global attractor to fractional order generalized coupled nonlinear Schrödinger equations with derivative

In this paper, we are concerned with the fractional Schrödinger equation with time fraction order, fractional Laplacian, and derivative terms. The existence of weak solution is established, as well as the exis...

Authors: Wenjing Song and Ganshan Yang

Ground state solutions for asymptotically periodic Schrödinger–Poisson systems involving Hartree-type nonlinearities

Authors: Lixi Wen and Sitong Chen

The quasi-boundary value regularization method for identifying the initial value with discrete random noise

In this paper, we study an inverse initial value problem for the fractional diffusion equation with discrete noise. This problem is ill-posed in the sense of Hadamard. We apply the trigonometric method in a no...

Authors: Fan Yang, Yan Zhang, Xiao-Xiao Li and Can-Yun Huang

Vanishing viscosity limit for Riemann solutions to zero-pressure gas dynamics with flux perturbation

In this paper, by the viscosity vanishing approach, we consider the Riemann problem for zero-pressure gas dynamics with flux perturbation. The Riemann solutions involve parameterized delta shock wave and const...

Authors: Yanyan Zhang and Jingen Yang

The stability analysis of a system with two delays

This paper presents new results of stability analysis for a linear system with two delays. We attempt to determine the asymptotic stability regions of the system in a parameter space by using D-partition metho...

Authors: Sertaç Erman, Hulya Kodal Sevindir and Ali Demir

On the well-posedness problem of the electrorheological fluid equations

Authors: Huashui Zhan

Existence and stability of periodic solutions for a forced pendulum with time-dependent damping

In this paper, we study the existence, multiplicity and stability of periodic solutions for a forced pendulum with time-dependent damping. The proof is based on the third order approximation method and a suita...

Authors: Fang-Fang Liao and Zaitao Liang

A discontinuous Sturm–Liouville problem with boundary conditions rationally dependent on the eigenparameter

The present paper deals with a class of discontinuous Sturm–Liouville problems with boundary conditions rationally dependent on the eigenparameter. Operator formulation is built and asymptotic formulas for eig...

Authors: Zhaowen Zheng, Jinming Cai, Kun Li and Maozhu Zhang

Infinitely many periodic solutions of planar Hamiltonian systems via the Poincaré–Birkhoff theorem

In this paper, we study the multiplicity of periodic solutions of one kind of planar Hamiltonian systems with a nonlinear term satisfying semilinear conditions. Using a generalized Poincaré–Birkhoff fixed poin...

Authors: Zaihong Wang and Tiantian Ma

Existence of positive periodic solutions for Liénard equations with an indefinite singularity of attractive type

Authors: Shiping Lu and Xingchen Yu

Positive solutions for integral boundary value problem of two-term fractional differential equations

Authors: Mengrui Xu and Zhenlai Han

Pullback attractors for non-autonomous reaction–diffusion equation with infinite delays in \(C_{\gamma,L^{r}(\Omega)}\) or \(C_{\gamma,W^{1,r}(\Omega)}\)

In this paper, the well-posedness for the non-autonomous reaction–diffusion equation with infinite delays on a bounded domain is established. The existence of pullback attractors for the process in

Authors: Yanping Ran and Jing Li

Qualitative analysis of a strongly coupled predator–prey system with modified Holling–Tanner functional response

In this paper, we deal with a strong coupled predator–prey model with modified Holling–Tanner functional response under homogeneous Neumann boundary conditions. We mainly discuss the following two problems: (1...

Authors: Rong Zeng

Two positive solutions for quasilinear elliptic equations with singularity and critical exponents

Authors: Yanbin Sang, Xiaorong Luo and Zongyuan Zhu

Multiple positive solutions for nonlinear coupled fractional Laplacian system with critical exponent

Authors: Maoding Zhen, Jinchun He, Haoyuan Xu and Meihua Yang

Infinitely many solutions for impulsive fractional boundary value problem with p-Laplacian

This paper deals with the existence of infinitely many solutions for a class of impulsive fractional boundary value problems with p-Laplacian. Based on a variant fountain theorem, the existence of infinitely many...

Authors: Yang Wang, Yansheng Liu and Yujun Cui

Blow-up and delay for a parabolic–elliptic Keller–Segel system with a source term

Authors: Yujuan Jiao and Wenjing Zeng

Three positive solutions for second-order periodic boundary value problems with sign-changing weight

Authors: Zhiqian He, Ruyun Ma and Man Xu

Bifurcation analysis for a free-boundary tumor model with angiogenesis and inhibitor

This paper is concerned with the bifurcation phenomenon of a free-boundary problem modeling the tumor growth under the action of angiogenesis and inhibitor. Taking the surface tension coefficient γ as a bifurcati...

Authors: Zejia Wang, Huijuan Song and Suzhen Xu

On the linear fuzzy model associated with Caputo–Fabrizio operator

In this paper, we introduce the fuzzy Caputo–Fabrizio operator under generalized Hukuhara differentiability concept. In this setting, we study the linear fuzzy fractional initial value problems and present the...

Authors: R. Abdollahi, A. Khastan, J. J. Nieto and R. Rodríguez-López