A global bifurcation theorem for convex-valued differential inclusions
type: Item
instance of: scholarly article
title: A global bifurcation theorem for convex-valued differential inclusions
zbMATH Open document ID: 1070.47045
DOI: 10.4171/ZAA/1198
author: S. Domachowski
author: Jacek Gulgowski
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2004-11-01T00:00:00Z
review text: The authors prove a global bifurcation theorem for convex-valued completely continuous maps. They prove as well an existence theorem for convex-valued differential inclusions with Sturm-Liouville boundary conditions \[ u''(t)\in\varphi(t,u(t),u'(t))\text{ for a.e., }t\in (a,b)\quad l(u)=0. \] The assumptions refer to the appropriate asymptotic behaviour of \(\varphi(t,x,y)\) for \(| x|+| y|\) close to 0 and to \(+\infty\), and they are independent from the Bernstein type conditions. In the last section, they give a set of examples of \(\varphi\) satisfying the assumptions of the theorem but not satisfying the Bernstein conditions.
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 2112820
zbMATH Keywords: differential inclusions
zbMATH Keywords: Sturm-Liouville conditions
zbMATH Keywords: global bifurcation
reviewed by: Ulrich Kosel
MaRDI profile type: Publication
cites work: Q3946833
cites work: Q5590339
cites work: Q4000472
cites work: Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')
cites work: Coincidence degree, and nonlinear differential equations
description: scientific article; zbMATH DE number 2112820