Bifurcation points of equations involving scalar nonlinear mappings in banach spaces^∗

^∗ This research was supported by the Alexander voil Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne

Abstract

Our results in [4] will be generalized to equations of the form:

and will be applied to the study of bifurcation points of equations involving scalar nonlinear mappings in Banach spaces of the form:

(The detailed intepretation will be given in the introduction). Supposing T0, for all λ, we shall show, under sufficient hypotheses on the mappings in this equation, that if λ is a characteristic value with multiplicity p of the pair (T, L₀} then (λ,O) is a bifurcation point and there exist at least 2_p different parameter families of nontrivial solutions in a neighborhood of (λo).

^∗ This research was supported by the Alexander voil Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne

^∗ This research was supported by the Alexander voil Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne

Notes

^∗ This research was supported by the Alexander voil Humboldt Foundation of the Federal Republic of Germany at the Mathematical Institute of the University of Cologne