中立型向量双曲偏微分方程的H-振动性  

H-OSCILLATION OF NEUTRAL VECTOR HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS

作　　者：罗李平[1] 俞元洪[2] 

机构地区：[1]衡阳师范学院数学与计算科学系,湖南衡阳421008 [2]中国科学院应用数学研究所,北京100080

出　　处：《数学杂志》2011年第5期893-898,共6页Journal of Mathematics

基　　金：国家自然科学天元基金资助项目(10626033);湖南省教育厅资助科研项目(07C164)

摘　　要：本文研究了一类中立型向量双曲偏微分方程边值问题的振动性.利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式正解的不存在性问题,获得了该类边值问题在Dirichlet边界条件下所有解H-振动的若干新的充分条件,其中H是Rm中的单位向量.In this article,we investigate the oscillations of boundary value problems for a class of neutral vector hyperbolic partial differential equations.By employing the concept of H-oscillation introduced by Domslak and the method of reducing dimension with scalar product,we reduce the multi-dimensional oscillation problems to the nonexistence problems of positive solutions of one-dimensional functional differential inequalities,some new sufficient conditions for the H-oscillation of all solutions of the boundary value problems are obtained under Dirichlet boundary condition,where H is a unit vector of R^m.

关 键 词：中立型 双曲型 向量偏微分方程 H-振动性 

分 类 号：O175.27[理学—数学]