Open Access
Translator Disclaimer
2007 Constant-sign and sign-changing solutions of a nonlinear eigenvalue problem involving the $p$-Laplacian
Siegfried Carl, Dumitru Motreanu
Differential Integral Equations 20(3): 309-324 (2007).

Abstract

For a certain range of the eigenvalue parameter we prove a new multiple and sign-changing solutions theorem. The novelties of our paper are twofold. First, unlike recent papers in the field we do not assume jumping nonlinearities and allow a rather general growth condition on the nonlinearity involved. Second, our approach strongly relies on a combined use of variational and topological arguments (e.g. critical points, mountain--pass theorem, second deformation lemma, variational characterization of the first and second eigenvalue of the p-Laplacian) on the one hand, and comparison principles for nonlinear differential inequalities, in particular, the existence of extremal constant-sign solutions, on the other hand.

Citation

Download Citation

Siegfried Carl. Dumitru Motreanu. "Constant-sign and sign-changing solutions of a nonlinear eigenvalue problem involving the $p$-Laplacian." Differential Integral Equations 20 (3) 309 - 324, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35109
MathSciNet: MR2293988

Subjects:
Primary: 35J60
Secondary: 35J20 , 35P30 , 47J05 , 47J30 , 58E05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
16 PAGES


SHARE
Vol.20 • No. 3 • 2007
Back to Top