Multiple global bifurcation branches for nonlinear Picard problems

J. Gulgowski, University of Gdansk, Gdansk, Poland

E. J. Qualitative Theory of Diff. Equ., No. 33. (2009), pp. 1-15.

Abstract: In this paper we prove the global bifurcation theorem for the nonlinear Picard problem. The right-hand side function $\varphi$ is a Caratheodory map, not differentiable at zero, but behaving in the neighbourhood of zero as specified in details below. We prove that in some interval $[a,b]\subset\real$ the Leray\--Schauder degree changes, hence there exists the global bifurcation branch. Later, by means of some approximation techniques, we prove that there exist at least two such branches.

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