Double linking theorem and multiple solutions

Abstract

In this paper, we establish a new double linking theorem: if two sets A and B link each other, then, under suitable conditions, we get two bounded (PS)-sequences which produce two distinct critical points. The critical points either have different critical values or belong to linking sets A and B separately. The abstract result will be used to solve semilinear eigenvalue problems and problems with jumping nonlinearities which may or may not resonant with respect to Fučı́k spectrum.