非光滑型对偶喷泉定理及其在一个微分包含问题中的应用

数学物理学报 ›› 2012, Vol. 32 ›› Issue (3): 530-539.

非光滑型对偶喷泉定理及其在一个微分包含问题中的应用

代国伟|王文婷|冯丽丽

西北师范大学数学与信息科学学院兰州 730070

收稿日期:2010-11-26 修回日期:2012-02-24 出版日期:2012-06-25 发布日期:2012-06-25
基金资助:
国家自然科学基金 (10971087) 和西北师范大学青年基金(NWNU-LKQN-10-21)资助

Nonsmooth Version of Dual Fountain Theorem and Its Application to a Differential Inclusion Problem

DAI Guo-Wei, WANG Wen-Ting, FENG Li-Li

Department of Mathematics, Northwest Normal University, Lanzhou 730070

Received:2010-11-26 Revised:2012-02-24 Online:2012-06-25 Published:2012-06-25
Supported by:
国家自然科学基金 (10971087) 和西北师范大学青年基金(NWNU-LKQN-10-21)资助

摘要/Abstract

摘要：

在这篇论文中, 作者应用非光滑分析理论把Willem^[16]建立的对偶喷泉定理推广到非光滑情形, 即非光滑型对偶喷泉定理. 作为该定理的应用,作者研究带有凹凸非线性项的Dirichlet 型微分包含问题的多解性.

关键词: 非光滑分析, 对偶喷泉定理, 微分包含问题, 凹凸非线性项

Abstract:

In this paper we establish a nonsmooth version of dual Fountain theorem by adopting the framework of nonsmooth analysis theory, which is a generalization of Theorem 3.18 of [16]. Then we present an application of this Theorem to a Dirichlet-type differential inclusion problem involving concave and convex nonlinearities.

Key words: Non-smooth analysis, Dual Fountain theorem, Differential inclusion problem, Concave and convex nonlinearities

中图分类号:

35J20

代国伟, 王文婷, 冯丽丽. 非光滑型对偶喷泉定理及其在一个微分包含问题中的应用[J]. 数学物理学报, 2012, 32(3): 530-539.

DAI Guo-Wei, WANG Wen-Ting, FENG Li-Li. Nonsmooth Version of Dual Fountain Theorem and Its Application to a Differential Inclusion Problem[J]. Acta mathematica scientia,Series A, 2012, 32(3): 530-539.

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