Existence of a pair of positive solutions for a class of nonlinear eigenvalue problems

摘要

In this paper, we consider a nonlinear elliptic equation driven by the p-Laplacian and with a parameter λ > 0. Using a combination of variational and degree theoretic methods, we show that there exists λ* > 0 such that, if λ > λ*, then the problem has two positive smooth solutions. Our result extends earlier ones by Rabinowitz (semilinear equations) and Guo (nonlinear equations).