A note on a resonance problem
- 1 January 1986
- journal article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 102 (1-2) , 1-7
- https://doi.org/10.1017/s030821050001444x
Abstract
Synopsis: In this paper, we prove the existence of at least one solution to the problem where ∆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.This publication has 0 references indexed in Scilit: