Articles

Head-on collision between capillary–gravity solitary waves

The present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is su...

Authors: Marin Marin and M. M. Bhatti

On solutions of a class of three-point fractional boundary value problems

Authors: Zhanbing Bai, Yu Cheng and Sujing Sun

Local existence and uniqueness of increasing positive solutions for non-singular and singular beam equation with a parameter

This paper is concerned with a class of beam equations with a parameter. By using the fixed point theorems of mixed monotone operator and the properties of cone, we study the non-singular and singular case, re...

Authors: Hui Wang and Lingling Zhang

Linear difference operator with multiple variable parameters and applications to second-order differential equations

Authors: Feifan Li, Zhonghua Bi, Shaowen Yao and Yun Xin

Superconvergence of the function value for pentahedral finite elements for an elliptic equation with varying coefficients

Authors: Jinghong Liu and Qiding Zhu

Regular approximation of singular Sturm–Liouville problems with eigenparameter dependent boundary conditions

In this paper we consider singular Sturm–Liouville problems with eigenparameter dependent boundary conditions and two singular endpoints. The spectrum of such problems can be approximated by those of the inher...

Authors: Maozhu Zhang, Kun Li and Hongxiang Song

Existence of ground state solutions for an asymptotically 2-linear fractional Schrödinger–Poisson system

Authors: Dandan Yang and Chuanzhi Bai

Multiple homoclinic solutions for p-Laplacian Hamiltonian systems with concave–convex nonlinearities

Authors: Lili Wan

Stability analysis and prevention strategies of tobacco smoking model

This research work is related to a tobacco smoking model having a significance class of users of tobacco in the form of snuffing. For this purpose, the formulation of the model containing snuffing class is pre...

Authors: Ebraheem Alzahrani and Anwar Zeb

New existence results for coupled delayed differential systems with multi-parameters

In this paper, several novel existence and multiplicity results are established for a coupled functional differential system with multi-parameters. The discussion is based upon fixed point theory, and our main...

Authors: Ruipeng Chen and Xiaoya Li

Nonlinear conservation laws for the Schrödinger boundary value problems of second order

In this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger bou...

Authors: Ming Ren, Shiwei Yun and Zhenping Li

Infinitely many high energy solutions for fractional Schrödinger equations with magnetic field

Authors: Libo Yang, Tianqing An and Jiabin Zuo

Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

Authors: Yongbin Wang and Binhua Feng

New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity

Authors: Mohammad M. Al-Gharabli

Positive bound state solutions for the nonlinear Schrödinger–Poisson systems with potentials

Authors: Jing Yang

Existence of solutions for some two-point fractional boundary value problems under barrier strip conditions

Authors: Zhiyu Li and Zhanbing Bai

Multiple periodic solutions for damped vibration systems with superquadratic terms at infinity

By using variational methods, we obtain infinitely many nontrivial periodic solutions for a class of damped vibration systems with superquadratic terms at infinity. By using some weaker conditions, our results...

Authors: Ping Li and Guanwei Chen

Convergence rates to the damped system of compressible adiabatic flow through porous media with boundary effect

In this paper, we consider convergence rates to solutions for the damped system of compressible adiabatic flow through porous media with boundary effect. Compared with the results obtained by Pan, the better c...

Authors: Lina Zhang, Shifeng Geng and Yuling Gao

Periodic solutions for second order damped boundary value problem with nonnegative Green’s functions

Authors: Yongxin Jiang

Penalty algorithm adapted for the spectral element discretization of the Darcy equations

Any spectral element discretization of the Darcy problem can be efficiently solved by applying the penalty method. This method leads to a system of equations with uncoupled unknowns. We prove a posteriori erro...

Authors: Mohamed Abdelwahed and Nejmeddine Chorfi

Upper and lower solution method for Hilfer fractional evolution equations with nonlocal conditions

This paper is concerned with the existence of extremal mild solutions for Hilfer fractional evolution equations with nonlocal conditions in an ordered Banach space E. By employing the method of lower and upper so...

Authors: Haide Gou and Yongxiang Li

On the existence of positive solutions for generalized fractional boundary value problems

The existence of positive solutions is established for boundary value problems defined within generalized Riemann–Liouville and Caputo fractional operators. Our approach is based on utilizing the technique of ...

Authors: Arjumand Seemab, Mujeeb Ur Rehman, Jehad Alzabut and Abdelouahed Hamdi

Existence of positive ground state solutions of Schrödinger–Poisson system involving negative nonlocal term and critical exponent on bounded domain

In this paper, we prove the existence of positive ground state solutions of the Schrödinger–Poisson system involving a negative nonlocal term and critical exponent on a bounded domain. The main tools are the m...

Authors: Wenxuan Zheng, Wenbin Gan and Shibo Liu

Stability of functional differential systems applied to the model of testosterone regulation

Authors: Alexander Domoshnitsky, Irina Volinsky, Olga Pinhasov and Marina Bershadsky

Basic theory of differential equations with linear perturbations of second type on time scales

In this paper, we develop the theory of differential equations with linear perturbations of second type on time scales. An existence theorem for differential equations with linear perturbations of second type ...

Authors: Yige Zhao, Yibing Sun, Zhi Liu and Zhanbing Bai

Maximum principle and its application to multi-index Hadamard fractional diffusion equation

This study establishes some new maximum principle which will help to investigate an IBVP for multi-index Hadamard fractional diffusion equation. With the help of the new maximum principle, this paper ensures t...

Authors: Xueyan Ren, Guotao Wang, Zhanbing Bai and A. A. El-Deeb

Blow-up for the sixth-order multidimensional generalized Boussinesq equation with arbitrarily high initial energy

In this paper, we consider the Cauchy problem for the sixth-order multidimensional generalized Boussinesq equation with double damping terms. By using the improved convexity method combined with Fourier transf...

Authors: Jianghao Hao and Aiyuan Gao

A condition for blow-up solutions to discrete p-Laplacian parabolic equations under the mixed boundary conditions on networks

Authors: Soon-Yeong Chung, Min-Jun Choi and Jaeho Hwang

Solvability of some boundary value problems involving p-Laplacian and non-autonomous differential operators

Authors: Milena Petrini

Spectral analysis of the matrix Sturm–Liouville operator

The self-adjoint matrix Sturm–Liouville operator on a finite interval with a boundary condition in general form is studied. We obtain asymptotic formulas for the eigenvalues and the weight matrices of the cons...

Authors: Natalia P. Bondarenko

On the Boussinesq system: local well-posedness of the strong solution and inviscid limits

In this paper, we consider the solvability, regularity and vanishing viscosity limit of the 3D viscous Boussinesq equations with a Navier-slip boundary condition. We also obtain the rate of convergence of the ...

Authors: Lianhong Guo, Yuanfei Li and Chunjuan Hou

Non-real eigenvalues of nonlocal indefinite Sturm–Liouville problems

The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite Sturm–Liouville differential equation with nonloca...

Authors: Fu Sun, Kun Li, Jiangang Qi and Baochao Liao

Sign-constancy of Green’s functions for impulsive nonlocal boundary value problems

Authors: A. Domoshnitsky and Iu. Mizgireva

Blow-up results for a quasilinear von Karman equation of memory type

In this paper, we consider the blow-up result of solution for a quasilinear von Karman equation of memory type with nonpositive initial energy as well as positive initial energy. For nonincreasing function

Authors: Mi Jin Lee and Jum-Ran Kang

Positive solutions to second-order singular nonlocal problems: existence and sharp conditions

Authors: Shiqi Ma and Xuemei Zhang

On a weak solution matching up with the double degenerate parabolic equation

Authors: Sujun Weng

Existence of solutions for a nonhomogeneous Dirichlet problem involving \(p(x)\)-Laplacian operator and indefinite weight

Authors: Aboubacar Marcos and Aboubacar Abdou

Uniqueness result for a fractional diffusion coefficient identification problem

In this paper, we establish an identifiability result for the coefficient identification problem in a fractional diffusion equation in a bounded domain from the observation of the Cauchy data on particular sub...

Authors: Fadhel Jday and Ridha Mdimagh

Existence of multiple positive solutions for nonhomogeneous fractional Laplace problems with critical growth

We prove the existence of multiple positive solutions of fractional Laplace problems with critical growth by using the method of monotonic iteration and variational methods.

Authors: Fang Wang and Yajing Zhang

A conservative numerical scheme for Rosenau-RLW equation based on multiple integral finite volume method

A multiple integral finite volume method combined and Lagrange interpolation are applied in this paper to the Rosenau-RLW (RRLW) equation. We construct a two-level implicit fully discrete scheme for the RRLW e...

Authors: Cui Guo, Fang Li, Wenping Zhang and Yuesheng Luo

Shape optimization of turbine blade cooling system using topological sensitivity analysis method

The topological sensitivity analysis method gives the variation of a criterion with respect to the creation of a small hole in the domain. In this paper, we use this method to solve an inverse problem related ...

Authors: Emna Ghezaiel, Maatoug Hassine, Mohamed Abdelwahed and Nejmeddine Chorfi

Higher integrability for weak solutions to a degenerate parabolic system with singular coefficients

Authors: Yan Dong, Guangwei Du and Kelei Zhang

Discontinuous generalized double-almost-periodic functions on almost-complete-closed time scales

In this paper, we introduce the concept of almost-complete-closed time scales (ACCTS) that allows independent variables of functions to possess almost-periodicity under translations. For this new type of time ...

Authors: Chao Wang, Ravi P. Agarwal, Donal O’Regan and Rathinasamy Sakthivel

The critical exponent for fast diffusion equation with nonlocal source

Authors: Chunxiao Yang, Linghua Kong, Yingxue Wu and Qing Tian

The dynamic properties of solutions for a nonlinear shallow water equation

The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation...

Authors: Yeqin Su, Shaoyong Lai and Sen Ming

Global large solutions to the planar magnetohydrodynamics equations with constant heat conductivity

This paper is concerned with global existence of large solutions to the initial-boundary value problem of the planar magnetohydrodynamic compressible flow. Under the assumptions that viscosity and heat conduct...

Authors: Wei Li and Zhaoyang Shang

A new application of Schrödinger-type identity to singular boundary value problem for the Schrödinger equation

In this paper, we present a modified Schrödinger-type identity related to the Schrödinger-type boundary value problem with mixed boundary conditions and spatial heterogeneities. This identity can be regarded a...

Authors: Bo Meng

Least energy sign-changing solutions for Kirchhoff–Poisson systems

Authors: Guoqing Chai and Weiming Liu

The existence of sign-changing solution for a class of quasilinear Schrödinger–Poisson systems via perturbation method

This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to t...

Authors: Lizhen Chen, Xiaojing Feng and Xinan Hao

Ground state solutions for Hamiltonian elliptic systems with super or asymptotically quadratic nonlinearity

Authors: Yubo He, Dongdong Qin and Dongdong Chen