Electron. J. Diff. Eqns., Vol. 2008(2008), No. 117, pp. 1-9.

An application of a global bifurcation theorem to the existence of solutions for integral inclusions

Stanislaw Domachowski

Abstract:
We prove the existence of solutions to Hammerstein integral inclusions of weakly completely continuous type. As a consequence we obtain an existence theorem for differential inclusions, with Sturm-Liouville boundary conditions,
$$\displaylines{ u''(t) \in -F(t,u(t),u'(t)) \quad\hbox{for a.e. } t\in(a,b) \cr l(u) = 0. }$$

Submitted April 17, 2008. Published August 25, 2008.
Math Subject Classifications: 47H04, 34A60, 34B24.
Key Words: Integral inclusion; differential inclusion; global bifurcation; selectors; Sturm-Liouville boundary conditions.

Show me the PDF file (234 KB), TEX file, and other files for this article.

Stanislaw Domachowski
Institute of Mathematics
University of Gdansk
ul. Wita Stwosza 57, 80-952 Gdansk, Poland
email: mdom@math.univ.gda.pl

Return to the EJDE web page