Lower bounds of Fucik eigenvalues of the weighted one dimensional p-Laplacian

Abstract

In this paper we obtain a family of curves bounding the region which contains all the non trivial Fucik eigenvalues of the weighted one dimensional p laplacian with Neumann boundary conditions. We obtain different proofs of the isolation result of the trivial lines, and the existence of a gap at infinity between the first curve and the trivial lines. We also give a lower bound for the eigenvalues of the p-Laplacian with Neumann boundary conditions.