Eigenvalue Problems for the p-Laplacian with Indefinite Weights
Date
2001-05-10
Authors
Cuesta, Mabel
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We consider the eigenvalue problem -∆pu = λV(x) |u|p-2 u, u ∈ W1,p0 (Ω) where p > 1, ∆p is the p-Laplacian operator, λ > 0, Ω is a bounded domain in ℝN and V is a given function in Ls (Ω) (s depending on p and N). The weight function V may change sign and has nontrivial positive part. We prove that the least positive eigenvalue is simple, isolated in the spectrum and it is the unique eigenvalue associated to a nonnegative eigenfunction. Furthermore, we prove the strict monotonicity of the least positive eigenvalue with respect to the domain and the weight.
Description
Keywords
Nonlinear eigenvalue problem, p-Laplacian, Indefinite weight
Citation
Cuesta, M. (2001). Eigenvalue problems for the p-Laplacian with indefinite weights. <i>Electronic Journal of Differential Equations, 2001</i>(33), pp. 1-9.