Existence of critical points for noncoercive functionals with critical Sobolev exponent

被引：2

作者：

Li, Zhouxin ^{[1
]}

Yuan, Xiang ^{[1
]}

Zhang, Qi ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha, Peoples R China

来源：

APPLICABLE ANALYSIS | 2022年 / 101卷 / 15期

基金：

中国国家自然科学基金;

关键词：

Critical points; noncoercive functional; critical Sobolev exponent; elliptic equations;

D O I：

10.1080/00036811.2021.1892078

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the following noncoercive functional with the critical Sobolev exponent I(u) = 1/2 integral(Omega)1/(1 + vertical bar u vertical bar)(2 alpha) vertical bar del u vertical bar(2)dx - lambda/q integral(Omega) vertical bar u vertical bar(q)dx - 1/2*(1 - alpha) integral(Omega) vertical bar u vertical bar(2)* (1- alpha) dx, where lambda > 0, 0 < alpha < (N + 2)/2N, 2 < q < 2* (1 - alpha), 2* = 2N/(N - 2). We prove the existence of a nontrivial critical point via the mountain pass theorem and the multiplicity via Clark's theorem.

引用

页码：5358 / 5375

页数：18

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