Conicting nonlinearities and spectral lacunae bounded on one side by eigenvalues
Hans-Jörg Ruppen · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2005
This paper deals with eigenvalue problems of the form where 0 λ 1 when λ is in a spectral lacuna . The existence of solutions depends on the weight of μ > 0. Moreover, when λ increases (while μ is kept fixed), some solutions are lost when crossing eigenvalues. The above results are derived with the help of an abstract approach based on variational techniques for multiple solutions. This approach can even be applied to a wider class of problems, the one presented herein being only a model problem.