Abstract and Applied Analysis

On the Fredholm Alternative for the Fučík Spectrum

Pavel Drábek and Stephen B. Robinson

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Abstract

We consider resonance problems for the one-dimensional p -Laplacian assuming Dirichlet boundary conditions. In particular, we consider resonance problems associated with the first three curves of the Fučík Spectrum. Using variational arguments based on linking theorems, we prove sufficient conditions for the existence of at least one solution. Our results are related to the classical Fredholm Alternative for linear operators. We also provide a new variational characterization for points on the third Fučík curve.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 125464, 20 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170937

Digital Object Identifier
doi:10.1155/2010/125464

Mathematical Reviews number (MathSciNet)
MR2754193

Zentralblatt MATH identifier
1214.47011

Citation

Drábek, Pavel; Robinson, Stephen B. On the Fredholm Alternative for the Fučík Spectrum. Abstr. Appl. Anal. 2010 (2010), Article ID 125464, 20 pages. doi:10.1155/2010/125464. https://projecteuclid.org/euclid.aaa/1313170937


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