Bulletin of the Belgian Mathematical Society - Simon Stevin

Multiplicity of Solutions for Doubly Resonant Neumann Problems

Michael E. Filippakis and Nikolaos S. Papageorgiou

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Abstract

In this paper,we examine semilinear Neumann problems which at $\pm\infty$ are resonant with respect to two successive eigenvalues (double resonance situation). Using variational methods based on the critical point theory together with Morse theory, we prove two multiplicity results. In the first we obtain two nontrivial solutions and in the second three, two of which have constant sign (one positive, the other negative).

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 1 (2011), 135-156.

Dates
First available in Project Euclid: 10 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1299766494

Digital Object Identifier
doi:10.36045/bbms/1299766494

Mathematical Reviews number (MathSciNet)
MR2809909

Zentralblatt MATH identifier
1220.35058

Subjects
Primary: 35J8015 35J85 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Keywords
Double resonance LL-condition Morse theory critical groups multiple solutions

Citation

Filippakis, Michael E.; Papageorgiou, Nikolaos S. Multiplicity of Solutions for Doubly Resonant Neumann Problems. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 1, 135--156. doi:10.36045/bbms/1299766494. https://projecteuclid.org/euclid.bbms/1299766494


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