Existence of the Eigenvalues for the Cone Degenerate p-Laplacian

Abstract

The present paper is concerned with the eigenvalue problem for cone degenerate p-Laplacian. First the authors introduce the corresponding weighted Sobolev s-paces with important inequalities and embedding properties. Then by adapting Lusternik-Schnirelman theory, they prove the existence of infinity many eigenvalues and eigenfunctions. Finally, the asymptotic behavior of the eigenvalues is given.