On a criterion for discrete or continuous spectrum of p-Laplace eigenvalue problems with singular sign-changing weights

摘要

In this paper we study the existence of spectrum for one-dimensional p-Laplace eigenvalue problems with singular weights subject to Dirichlet boundary condition. For certain class of singular sign-changing weights, we prove the existence of discrete spectrum. Pr oofs are based on the C1T0; 1U-regularity of solutions and construction of the first eigenvalue in a variational set-up. We also present an example of a weight for which the spectrum is continuous and any corresponding eigenfunction does not belong to C1T0; 1U.