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A note on a resonance problem
- Source :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 102:1-7
- Publication Year :
- 1986
- Publisher :
- Cambridge University Press (CUP), 1986.
-
Abstract
- SynopsisIn this paper, we prove the existence of at least one solution to the problemwhere ∆k is an eigenvalue of the linear part, h is orthogonal to the eigenspace corresponding to ∆R and g is a nonlinear perturbation which can be, for instance, a continuous periodic real function with mean value zero. We employ the techniques used by the second author in a previous paper in which the same result was obtained in the case in which ∆R is assumed to be simple. The final result is obtained by using variational methods and in particular a suitable version of the saddle point theorem of P. Rabinowitz.
Details
- ISSN :
- 14737124 and 03082105
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Accession number :
- edsair.doi...........9417bb36e38cdb980ae0a0c4f399c0f5