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.
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页码：5358 / 5375
页数：18
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