Carlos C. Aranda, Enrique Lami Dozo
This article concerns the existence of multiple solutions for the problem
where is a smooth, bounded domain in with , , , , , and are real positive numbers, and is a positive real valued and measurable function. We start with the case and by studying the structure of the range of . Our method to build 's which give at least two solutions is based on positive and negative principal eigenvalues with weight. For small positive and for values of the parameters in finite intervals, we find multiplicity via estimates on the bifurcation set.
Submitted August 12, 2007. Published January 2, 2008.
Math Subject Classifications: 35J25, 35J60.
Key Words: Bifurcation; weighted principal eigenvalues and eigenfunctions.
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| Carlos C. Aranda |
Universidad Nacional de Formosa, Argentina
| Enrique Lami Dozo |
CONICET-Universidad de Buenos Aires, Argentina.
and Univ. Libre de Bruxelles, Belgium
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