具连续分布变元的向量抛物型方程振动性的新准则

数学季刊 ›› 2011, Vol. 26 ›› Issue (2): 260-264.

具连续分布变元的向量抛物型方程振动性的新准则

1. Department of Mathematics and Computational Science, Hengyang Normal University2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences

收稿日期:2008-03-05 出版日期:2011-06-30 发布日期:2023-05-05
作者简介:LI Yuan-dan(1971-), male, native of Hengnan, Hunan, a lecturer of Hengyang Normal University, engages in oscillation theory of diﬀerential equation.
基金资助:
Supported by the Science Research Foundation of Administration of Education of Hunan Province(07C164)；

New Criteria for Oscillation of Vector Parabolic Equations with Continuous Distribution Arguments

1. Department of Mathematics and Computational Science, Hengyang Normal University2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Received:2008-03-05 Online:2011-06-30 Published:2023-05-05
About author:LI Yuan-dan(1971-), male, native of Hengnan, Hunan, a lecturer of Hengyang Normal University, engages in oscillation theory of diﬀerential equation.
Supported by:
Supported by the Science Research Foundation of Administration of Education of Hunan Province(07C164)；

摘要/Abstract

摘要： The oscillations of a class of vector parabolic partial diﬀerential equations with continuous distribution arguments are studied. By employing the concept of H-oscillation and the method of reducing dimension with inner product, the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional diﬀerential inequalities have not eventually positive solution. Some new suﬃcient conditions for the Hoscillation of all solutions of the equations are obtained under Dirichlet boundary condition, where H is a unit vector of R^M.

关键词: H-oscillation, vector, parabolic equation, continuous distribution argument

Abstract: The oscillations of a class of vector parabolic partial diﬀerential equations with continuous distribution arguments are studied. By employing the concept of H-oscillation and the method of reducing dimension with inner product, the multi-dimensional oscillation problems are changed into the problems of which one-dimensional functional diﬀerential inequalities have not eventually positive solution. Some new suﬃcient conditions for the Hoscillation of all solutions of the equations are obtained under Dirichlet boundary condition, where H is a unit vector of R^M.

Key words: H-oscillation, vector, parabolic equation, continuous distribution argument

中图分类号:

O175.26

李元旦, 罗李平, 俞元洪. 具连续分布变元的向量抛物型方程振动性的新准则[J]. 数学季刊, 2011, 26(2): 260-264.

LI Yuan-dan, LUO Li-ping, YU Yuan-hong. New Criteria for Oscillation of Vector Parabolic Equations with Continuous Distribution Arguments [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(2): 260-264.

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