Yuan, Hairong
Published in
Acta Mathematica Scientia

We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting be...

Ren, Yanbo
Published in
Acta Mathematica Scientia

In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ∫{f*>λ}Φ1(λw1)w2dP⩽C∫ΩΦ2(C|f∞|w3)w4dP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidema...

Almahalebi, Muaadh Chahbi, Abdellatif
Published in
Acta Mathematica Scientia

The aim of this paper is to introduce and solve the p-radical functional equation f(xp+ypp)=f(x)+f(y),p∈N2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f\left( {\sqr...

Zheng, Weishan Chen, Yanping
Published in
Acta Mathematica Scientia

In this article, we study the Volterra integral equations with two kinds of delay that are proportional delay and nonproportional delay. We mainly use Chebyshev spectral collocation method to analyze them. First, we use variable transformation to transform the equation into an new equation which is defined in [−1, 1]. Then, with the help of Gronwal...

Schulz, Simon
Published in
Acta Mathematica Scientia

We show that any smooth solution (u, H) to the stationary equations of magneto-hydrodynamics belonging to both spaces L6(ℝ3) and BMO−1(ℝ3) must be identically zero. This is an extension of previous results, all of which systematically required stronger integra-bility and the additional assumption ∇u,∇H ∈ L2(ℝ3), i.e., finite Dirichlet integral.

Youkana, Abderrahmane Messaoudi, Salim A. Guesmia, Aissa
Published in
Acta Mathematica Scientia

We consider a quasilinear heat system in the presence of an integral term and establish a general and optimal decay result from which improves and generalizes several stability results in the literature.

Yang, Xianyong Zhang, Wei Zhao, Fukun
Published in
Acta Mathematica Scientia

In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in ℝN which includes the so-called modified nonlinear Schrödinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.

Qiu, Jinghui
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...

Ma, Wen-Xiu
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,...

Wang, Changyou Li, Nan Zhou, Yuqian Pu, Xingcheng Li, Rui
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...