JournalszaaVol. 23, No. 2pp. 275–292

A Global Bifurcation Theorem for Convex-Valued Differential Inclusions

  • S. Domachowski

    University of Gdansk, Poland
  • J. Gulgowski

    University of Gdansk, Poland
A Global Bifurcation Theorem for Convex-Valued Differential Inclusions cover
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Abstract

\newcommand\f{\phi} 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

u(t)\f(t,u(t),u(t))  for a.e.  t(a,b)u''(t) \in \f(t,u(t),u'(t))\ \ \hbox{for a.e.}\ \ t \in (a,b)
l(u)=0l(u) = 0

The assumptions refer to the appropriate asymptotic behaviour of \f(t,x,y)\f(t,x,y) for x+y|x| + |y| close to 00 and to ++\infty, and they are independent from the well known Bernstein-type conditions. In the last section we give a set of examples of \f\f 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