Solutions for elliptic equations with competing potentials in 4 dimensions
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 \(K(r_0,y_0'' )>0\). For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/21/abstr.html
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Electronic Journal of Differential Equations
- Volume
- 2026
- Issue
- 01-??
- Pages
- 21–21
- Publication date
- 2 March 2026
- Language
- EN