Article ID Journal Published Year Pages File Type
4663542 Acta Mathematica Scientia 2015 36 Pages PDF
Abstract

In this paper, we consider the following nonlinear elliptic problem : , in Ω, Δu = u = 0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n∈{5,6,7}, μ is a parameter and q ∈]4/(n−4),(12−n)/(n−4)[. We study the solutions which concentrate around two points of Ω. We prove that the concentration speeds are the same order and the distances of the concentration points from each other and from the boundary are bounded. For Ω = (Ωα)α a smooth ringshaped open set, we establish the existence of positive solutions which concentrate at two points of Ω. Finally, we show that for μ > 0, large enough, the problem has at least many positive solutions as the Ljusternik-Schnirelman category of Ω.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)