A Global Bifurcation Theorem for Convex-Valued Differential Inclusions

  • S. Domachowski

    University of Gdansk, Poland
  • J. Gulgowski

    University of Gdansk, Poland

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