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

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 $\mathbf{R}^N$ with $N\geq 4$. For $0<\lambda<\pi^2$, we show that the number of nonrotationally equivalent nonradial solutions tends to infinity as the inner radius of the domain tends to infinity.