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Start Over Subject measurable multifunction

1. Monotone approximation of measurable multifunctions by simple multifunctions

Creator:
Kubiś, Beata
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
measurable multifunction, Marczewski function, Vietoris topology, and simple multifunction
Language:
English
Description:
We investigate the problem of approximation of measurable multifunctions by monotone sequences of measurable simple ones. Our main tool is the Marczewski function, i.e., the characteristic function of a sequence of sets.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Nonlinear boundary value problems for second order differential inclusions

Creator:
Kyritsi , Sophia Th., Matzakos, Nikolaos, and Papageorgiou, Nikolaos S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
measurable multifunction, usc and lsc multifunction, and maximal monotone operator
Language:
English
Description:
In this paper we study two boundary value problems for second order strongly nonlinear differential inclusions involving a maximal monotone term. The first is a vector problem with Dirichlet boundary conditions and a nonlinear differential operator of the form $x\mapsto a(x,x^{\prime })^{\prime }$. In this problem the maximal monotone term is required to be defined everywhere in the state space $\mathbb{R}^N$. The second problem is a scalar problem with periodic boundary conditions and a differential operator of the form $x\mapsto (a(x)x^{\prime })^{\prime }$. In this case the maximal monotone term need not be defined everywhere, incorporating into our framework differential variational inequalities. Using techniques from multivalued analysis and from nonlinear analysis, we prove the existence of solutions for both problems under convexity and nonconvexity conditions on the multivalued right-hand side.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public