A Global Bifurcation Theorem for Convex-Valued Differential Inclusions
S. Domachowski
University of Gdansk, PolandJ. Gulgowski
University of Gdansk, Poland
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Abstract
We prove a global bifurcation theorem for convex-valued completely continuous maps. Basing on this theorem we prove an existence theorem for convex-valued differential inclusions with Sturm–Liouville boundary conditions
The assumptions refer to the appropriate asymptotic behaviour of for close to and to , and they are independent from the well known Bernstein-type conditions. In the last section we give a set of examples of satisfying the assumptions of the given theorem but not satisfying the Bernstein conditions.
Cite this article
S. Domachowski, J. Gulgowski, A Global Bifurcation Theorem for Convex-Valued Differential Inclusions. Z. Anal. Anwend. 23 (2004), no. 2, pp. 275–292
DOI 10.4171/ZAA/1198