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

الملخص EN

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 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.