On the eigenvalue problem involving the weighted p-Laplacian in radially symmetric domains

Abstract

We investigate the following eigenvalue problem, λ > 0 is a parameter, the weights L and K are measurable with L positive a.e. in A R2 R1 and K possibly sign-changing in A R2 R1 . We prove the existence of the first eigenpair and discuss the regularity and positiveness of eigenfunctions. The asymptotic estimates for u(x) and ∇u(x) as |x| → R + 1 or R − 2 are also investigated.

Concave-Convex Problems for the Robin p-Laplacian Plus an Indefinite Potential

“…Drábek-Hernández [12] studied quasilinear eigenvalue problems with singular weights driven by the p-Laplacian. Drábek-Ho-Sarkar considered an eigenvalue problem involving the weighted p-Laplacian in radially symmetric domains [13] and the Fredholm alternative for the p-Laplacian in exterior domains [14]. , using the fibrering method, proved the existence of multiple positive solutions to quasilinear problems of second order driven by the p-Laplacian and also proved nonexistence results.…”