[毕业论文] 无穷多临界点的收敛性质 [复制链接]

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毕业论文-无穷多临界点的收敛性质，共63页，

我们知道，对称山路定理可以得到${\bf

C}^1$泛函的无穷多个临界值。而最近，Ryuji

Kajikiya在文章\cite{RK}中不仅证明了这无穷多个临界值收敛到零，而且证明了满足相同条件的泛函有收敛到零的临界点序列。

在这篇文章中，我们先简要地介绍了Ljusternik-Schnirelmann亏格理论；然后回顾了文章\cite{RK}中的已有结果和证明的思路，

以及由张恭庆建立的局部Lipschitz泛函的Minimax理论。最后，我们尝试着将Ryuji

Kajikiya的结果推广到局部Lipschitz泛函的情形。

并且在一定的条件下，我们得到了收敛到零的临界点序列。

It's well known that we can obtain infinitely many

critical values of a ${\bf C}^1$ functional by the Symmetric

Mountain Pass Theorem. Recently, in Ryuji Kajikiya \cite{RK}, the

author has proved not only that the infinitely many critical values

will converge to zero, but also that there exists an critical point

sequence converging to zero. In this article, we first give a brief

introduction to the Ljusternik-Schnirelmann genus theory, and then

we review the main results and the main line of the proofs in the

article \cite{RK}, we also review the Minimax theory of the locally

Lipschitz functionals given by K.C.Chang. After that we try to

generalize the result of Ryuji Kajikiya to the case of a locally

Lipschitz functional. And under certain conditions, we get the

critical point sequence which converges to zero.

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• 毕业论文-无穷多临界点的收敛性质
• 毕业论文-无穷多临界点的收敛性质.doc  [2.00MB]