## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Multiplicity of Solutions for Doubly Resonant Neumann Problems

#### 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

https://projecteuclid.org/euclid.bbms/1299766494

Digital Object Identifier
doi:10.36045/bbms/1299766494

Mathematical Reviews number (MathSciNet)
MR2809909

Zentralblatt MATH identifier
1220.35058

#### 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