Fine multibubble analysis in the higher-dimensional Brezis-Nirenberg problem
This article is concerned with the study of positive solutions to \(-\Delta u+\varepsilon V u=N(N-2)u^{\frac{N+2}{N-2}}\) in a bounded open set \(\Omega\subset\mathbb{R}^N\), \(N\geq 4\). The solutions are assumed to satisfy an homogeneous Dirichlet boundary condition while the potential \(V\in C^1(\overline{\Omega})\) is negative. The main result of the article establishes the existence of solutions exhibiting multiple concentration points. It is shown that such concentration points are isolated and the authors provide a characterization of the vector of these points as a critical point of a suitable function derived from the Green function of \(-\Delta\) on \(\Omega\).
existence of solutions with multiple concentration points
scientific article; zbMATH DE number 7896319
scientific article