Articles

An oscillation theorem for the nonlinear degenerate elliptic equation in the Heisenberg group

Authors: Duan Wu and Pengcheng Niu

Three solutions for a partial discrete Dirichlet boundary value problem with p-Laplacian

By employing critical point theory, we investigate the existence of solutions to a boundary value problem for a p-Laplacian partial difference equation depending on a real parameter. To be specific, we give preci...

Authors: Shaohong Wang and Zhan Zhou

Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

In this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorem...

Authors: Jian Liu and Wenguang Yu

An inverse problem of reconstructing option drift rate from market observation data

Drift rate is a very important parameter in the evolution of stock price, which has significant impact on the corresponding option pricing. This paper deals with an inverse problem of recovering the drift func...

Authors: Z. C. Deng, X. Y. Zhao and L. Yang

Fujita type theorem for a class of coupled quasilinear convection–diffusion equations

In this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the in...

Authors: Yanan Zhou, Yan Leng and Yuanyuan Nie

New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

In this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and compar...

Authors: Osama Moaaz, Choonkil Park, Elmetwally M. Elabbasy and Waed Muhsin

Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

In the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using...

Authors: Cholticha Nuchpong, Sotiris K. Ntouyas, Devaraj Vivek and Jessada Tariboon

Traveling wave solutions for a class of reaction-diffusion system

In this paper we investigate the existence of traveling wave for a one-dimensional reaction diffusion system. We show that this system has a unique translation traveling wave solution.

Authors: Bingyi Wang and Yang Zhang

Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms

By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the pe...

Authors: Haiyan Lv and Guanwei Chen

Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, t...

Authors: Hong Qiu, Wenmin Deng and Mingqi Xiang

Uniqueness and concentration for a fractional Kirchhoff problem with strong singularity

Authors: Shengbin Yu and Jianqing Chen

The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

Authors: Limei Dai and Huihui Cheng

Uniform estimates with data from generalized Lebesgue spaces in periodic structures

We study various types of uniform Calderón–Zygmund estimates for weak solutions to elliptic equations in periodic homogenization. A global regularity is obtained with respect to the nonhomogeneous term from we...

Authors: Yunsoo Jang

Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

A priori bounds were derived for the flow in a bounded domain for the viscous-porous interfacing fluids. We assumed that the viscous fluid was slow in

Authors: Yuanfei Li, Shuanghu Zhang and Changhao Lin

Ground state solutions for Kirchhoff-type equations with general nonlinearity in low dimension

Authors: Jing Chen and Yiqing Li

A study on controllability of impulsive fractional evolution equations via resolvent operators

In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theor...

Authors: Haide Gou and Yongxiang Li

Retraction Note: Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions

This article has been retracted. Please see the Retraction Notice for more detail: https://​doi.​org/​10.​1186/​s13661-021-01502-z

Authors: Yisheng Hu, Songhai Qin, Zhibin Liu and Yi Wang

Regularity criterion for 3D nematic liquid crystal flows in terms of finite frequency parts in \(\dot{B}_{\infty,\infty }^{-1}\)

Authors: Xiaoli Chen and Haiyan Cheng

Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

In this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parame...

Authors: S. Heidari and A. Razani

Local well-posedness of the inertial Qian–Sheng’s Q-tensor dynamical model near uniaxial equilibrium

We consider the inertial Qian–Sheng’s Q-tensor dynamical model for the nematic liquid crystal flow, which can be viewed as a system coupling the hyperbolic-type equations for the Q-tensor parameter with the incom...

Authors: Xiaoyuan Wang, Sirui Li and Tingting Wang

Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems t...

Authors: Yanbin Sang and Luxuan He

First order differential systems with a nonlinear boundary condition via the method of solution-regions

In this article we extend the known theory of solution regions to encompass nonlinear boundary conditions. We both provide results for new boundary conditions and recover some known results for the linear case.

Authors: Marlène Frigon, Marcos Tella and F. Adrián F. Tojo

Multiple solutions for a coercive quasilinear elliptic equation via Morse theory

We study the quasilinear elliptic problem which is resonant at zero. By using Morse theory, we obtain five nontrivial solutions for the equation with coercive nonlinearities.

Authors: Lifang Fu and Mingzheng Sun

On a doubly degenerate parabolic equation with a nonlinear damping term

Authors: Wenbin Xu

New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

A type of non-Newtonian filtration equations with variable delay is considered. Using a new approach which was established by Ge and Ren in (Nonlinear Anal. 58:477–488, 2004), we obtain the existence of periodic ...

Authors: Mei Xu and Bo Du

Analysis of reaction–diffusion systems where a parameter influences both the reaction terms as well as the boundary

Authors: A. Acharya, N. Fonseka and R. Shivaji

Random attractor for second-order stochastic delay lattice sine-Gordon equation

Authors: Xintao Li, Lianbing She and Zhenpei Shan

Positive ground states for nonlinearly coupled Choquard type equations with lower critical exponents

Authors: Huiling Wu

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