Published in Acta Mathematica Scientia
In this article, we extend the cyclic antimonotonicity from scalar bifunctions to vector bifunctions. We find out a cyclically antimonotone vector bifunction can be regarded as a family of cyclically antimonotone scalar bifunctions. Using a pre-order principle (see Qiu, 2014), we prove a new version of Ekeland variational principle (briefly, denote...
Published in Acta Mathematica Scientia
Based on a 4 × 4 matrix spectral problem, an AKNS soliton hierarchy with six potentials is generated. Associated with this spectral problem, a kind of Riemann-Hilbert problems is formulated for a six-component system of mKdV equations in the resulting AKNS hierarchy. Soliton solutions to the considered system of coupled mKdV equations are computed,...
Published in Acta Mathematica Scientia
This article is focusing on a class of multi-delay predator-prey model with feedback controls and prey diffusion. By developing some new analysis methods and using the theory of differential inequalities as well as constructing a suitable Lyapunov function, we establish a set of easily verifiable sufficient conditions which guarantee the permanence...
Published in Acta Mathematica Scientia
We concentrate on using the traceless Ricci tensor and the Bochner curvature tensor to study the rigidity problems for complete Kähler manifolds. We derive some elliptic differential inequalities from Weitzenb¨ock formulas for the traceless Ricci tensor of Kähler manifolds with constant scalar curvature and the Bochner tensor of Kähler-Einstein man...
Published in Acta Mathematica Scientia
This paper is devoted to the quasilinear equation {−div(w1|∇u|p−2∇u)=w2f(u)inΩ,u=0on∂Ω,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ \begin{gathered}- div\lef...
Published in Acta Mathematica Scientia
In this article, we study the blow-up phenomena of generalized double dispersion equations utt − uxx − uxxt + uxxxx − uxxtt = f(ux)x. Under suitable conditions on the initial data, we first establish a blow-up result for the solutions with arbitrary high initial energy, and give some upper bounds for blow-up time T* depending on sign and size of in...
Published in Acta Mathematica Scientia
In this article, we study the electromagnetic fluid system in three-dimensional whole space ℝ3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp − Lq estimates for the linearized equat...
Published in Acta Mathematica Scientia
The goal of the present paper is to investigate an abstract system, called fractional differential variational inequality, which consists of a mixed variational inequality combined with a fractional evolution equation in the framework of Banach spaces. Using discrete approximation approach, an existence theorem of solutions for the inequality is es...
Published in Acta Mathematica Scientia
Taking a class of linear (4+1)-dimensional partial differential equations as examples, we would like to show that there exist lump solutions and interaction solutions in (4+1)-dimensions. We will compute abundant lump solutions and interaction solutions to the considered linear (4+1)-dimensional partial differential equations via symbolic computati...
Published in Acta Mathematica Scientia
In this paper, we study the low Mach number limit of a compressible non-isothermal model for nematic liquid crystals in a bounded domain. We establish the uniform estimates with respect to the Mach number, and thus prove the convergence to the solution of the incompressible model for nematic liquid crystals.
