非光滑泛函临界点理论的一个应用  

An Application of Nonsmooth Critical Point Theory

作　　者：位继伟[1] 刘嘉荃[1] 

机构地区：[1]北京大学数学学院

出　　处：《数学进展》2002年第3期229-236,共8页Advances in Mathematics（China）

摘　　要：本文利用局部Lipschitz泛函的临界点理论,来得到一个改进的半线性方程的Landesman-Lazer型结果.问题来自于力学,称为变分不等式的特征值问题.在[3]中,D.Goeleven,D.Motreanu和P.D.Panagiotopoulos等人讨论了共振的情形,并得到了弱解的存在性的结果.但是,在他们结论中(见[3]中定理4.1);条件(H1)与(H2)却是互不相容的.本文得到了变分不等式的特征值问题在共振情形下的弱解存在性的相应结果.In this paper we seek for an improved Landesman-Lazer result on a kind of semi-linear partial differential equations. The proposed problem was motivated in the mechanics where the problem is to find an eigenvalue solution to the so-called variational inequality. In a preceeding paper, D. Goeleven, D. Motreanu and P. D. Panagiotopoulos reached an existence result of a weak solution to the variational inequality in resonant case. Howerer, there is an intrinsic contradiction in the conditions of their main theorem. We prove a similar existence result which is the rectification of the main theorem in the afore-mentioned paper.

关 键 词：非光滑泛函 临界点理论 局部Lipschitz泛函 特征值问题 半线性偏微分方程 变分不等式 

分 类 号：O177[理学—数学] O175.2[理学—基础数学]