Bifurcation from Infinity and Resonance Results at High Eigenvalues in Dimension One

Abstract

This paper is devoted to two different but related tags: firstly, the side of the bifurcation from infinity at every eigenvalue of the problem−u″(t)=λu(t)+g(t,u(t)),u∈H01(0,π), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearitygwe obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.