Title

On the Oscillations of the Solution Curve for A Class of Semilinear Equations

Document Type

Article

Publication Date

9-2006

Abstract

We consider positive solutions of the Dirichlet problem

where B is unit ball in Rn, λ is a positive parameter. Let λ1 denote the principal eigenvalue of the Laplacian on B with zero boundary conditions. We show that for 1⩽n⩽5 the problem has infinitely many positive solutions at λ=λ1, while for n⩾6 the problem has at most finitely many solutions at any λ.

DOI

dx.doi.org/10.1016/j.jmaa.2005.08.074