具有一般边界的Hilbert流形上的变分不等式解的存在性及拓扑性质

The Existence and Topological Property of the Solutions for Variational Inequality in the Hilbert Manifold with General Boundary

本文的主要目的是首先建立具有一般边界的Hilbert流形的概念.然后,借助于临界点理论的思想方法,讨论在这种流形上的变分不等式解的存在性以及解的局部拓扑性质,最后给出了Morse不等式.

The main purpose of this paper is first to establish the concept ofHilbert manifolds with general boundary, and then, by use of the methodof the critical point theory, consider the existence and the local topologicalproperty of the solutions for a class of variational inequalities in thismanifold. At last, the famous Morse inequality is deduced.