Existence of many positive solutions of semilinear elliptic equations on an annulus

Abstract

This paper is concerned with multiplicity of positive nonradial solutions of a nonlinear eigenvalue problem on an expanding annulus domain with a fixed width in R N \mathbf {R}^N with N ≥ 4 N\geq 4 . For 0 > λ > π 2 0>\lambda >\pi ^2 , we show that the number of nonrotationally equivalent nonradial solutions tends to infinity as the inner radius of the domain tends to infinity.