发展型H-半变分不等式解的存在性(英文)  

Existence Results for Evolution Hemivariational Inequalities

作　　者：刘振海[1] Simon L 

机构地区：[1]长沙电力学院数学系 [2]匈牙利EOTVOS大学

出　　处：《数学进展》2001年第1期47-55,共9页Advances in Mathematics（China）

基　　金：Natural Science Foundation of Hunan Province.

摘　　要：本文研究非线性发展型Ｈ－半变分不等式，即具有非凸泛函的抛物型变分不等式．这类问题的研究起源于力学．利用Ｃｌａｒｋｅ广义梯度和（Ｓ＋）型多值映象的不动点理论，我们证明了这类问题解的存在性．并利用这一理论，研究了具间断项的非线性抛物型方程解的存在性．In this paper, we deal with nonlinear evolution hemivariational inequalities as a generalization to nonconvex functionals of the parabolic variational inequalities. This extension is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of multivalued (S+) type mappings, we show that there exists at least one solution and present applications of the abstract theory to parabolic equations with discontinuous nonlinearities.

关 键 词：发展H-半变分不等式 多值映象 周期解 解 存在性 非线性抛物型方程 

分 类 号：O178[理学—数学] O175.26[理学—基础数学]