Wanli Sun, Yiding Wang, Jianjun Nie
Abstract:
We study the elliptic equation with competing potentials
$$\displaylines{
-\Delta u+V(y)u=K(y)u^{2^*-1}, \quad \text{in } H^1(\mathbb{R}^N), \cr
u>0, \quad y \in \mathbb{R}^N,
}$$
where \(2^*=\frac{2N}{N-2}\) is the critical Sobolev exponent,
\(y=(y',y'')\in \mathbb{R}^2\times\mathbb{R}^{N-2}\), \(V(|y'|,y'')\) and \(K(|y'|,y'')\)
are nonnegative and bounded functions.
Using a finite dimensional reduction argument and local Pohozaev identities,
we prove the existence infinitely many solutions,
when \(N=4\), \(K(r,y'')\) has a stable critical
point \((r_0,y_0'')\) with \(r_0>0\) and \(K(r_0,y_0'')>0\).
Submitted December 24, 2025. Published March 2, 2026.
Math Subject Classifications: 35J15, 35J20.
Key Words: Critical elliptic equation; local Pohozaev identities; competing potentials; infinitely many solutions,
DOI: 10.58997/ejde.2026.21
Show me the PDF file (413 KB), TEX file for this article.
 |
Wanli Sun School of Mathematics and Physics North China Electric Power University Beijing 102206, China email: 15215090646@163.com |
|---|---|
 |
Yiding Wang School of Mathematics and Physics North China Electric Power University Beijing 102206, China email: wyd1285077293@outlook.com |
 |
Jianjun Nie School of Mathematics and Physics North China Electric Power University Beijing 102206, China email: niejjun@126.com |
Return to the EJDE web page