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

Wang, Zhi-Qiang; Willem, Michel

doi:10.1090/S0002-9939-99-04708-5

Existence of many positive solutions of semilinear elliptic equations on an annulus
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by Zhi-Qiang Wang and Michel Willem PDF

Proc. Amer. Math. Soc. 127 (1999), 1711-1714 Request permission

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 $\mathbf {R}^N$ 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.

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