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

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) = lambda u(t) + g(t, u(t)), u is an element of H-0(1)(0, pi), secondly, the solutions of the associated resonant problem at any eigenvalue. From the global shape of the nonlinearity g we obtain computable integral values which will decide the behavior of the bifurcations and, consequently, the possibility of finding solutions of the resonant problems.