拟线性椭圆方程的分歧问题

我们对一类拟线性椭圆方程讨论Rabinowitz型的分歧定理。不动点定理被用来实现有穷维约化过程。     

一类奇异二阶边值问题的正解

讨论奇异二阶边值问题，设非线性项在原点和无究远处跨越相应奇异线性问题的第一特征值。利用变分方法证明了问题至少有一正解。     

多重临界点存在定理及其应用

熟知对于满足P.S.条件的c~1函数f,如果能找到适当的挽着,就可以利用极小极大原理得到临界值,另一方面如果f又是下方有界的,那末f必达到最小值。我们首先证明这时至少有三个临界点。     

MORSE THEORY UNDER GENERAL BOUNDARY CONDITIONS

Morse inequalities for Morse functions under general boundary conditions were initiallystudied by Morse and Van Schaa(?)k.It is our purpose to present a natural extension of the theorem dueto Morse and Van Schaack with a considerably slmplified proof.     

THE MORSE INDEX OF A SADDLE POINT

This paper is devoted to clarifying the relationship between the classical Morse theory andthe Mountain Pass Lemma via the local linking concept.It is shown that for a C~1-function f with alocal linking,the m-thcritical group is nontrivial,where m is the Morse index.Combined with thebehavior of f at infinity,this result can be used to offer the existence of nontrivial critical points.