Displaying similar documents to “On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints”

Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')

L. H. Erbe, W. Krawcewicz (1991)

Annales Polonici Mathematici

Similarity:

Applying the topological transversality method of Granas and the a priori bounds technique we prove some existence results for systems of differential inclusions of the form y'' ∈ F(t,y,y'), where F is a Carathéodory multifunction and y satisfies some nonlinear boundary conditions.

A strong relaxation theorem for maximal monotone differential inclusions with memory

Nikolaos S. Papageorgiou (1994)

Archivum Mathematicum

Similarity:

We consider maximal monotone differential inclusions with memory. We establish the existence of extremal strong and then we show that they are dense in the solution set of the original equation. As an application, we derive a “bang-bang” principle for nonlinear control systems monitored by maximal monotone differential equations.

Extremal solutions and relaxation for second order vector differential inclusions

Evgenios P. Avgerinos, Nikolaos S. Papageorgiou (1998)

Archivum Mathematicum

Similarity:

In this paper we consider periodic and Dirichlet problems for second order vector differential inclusions. First we show the existence of extremal solutions of the periodic problem (i.e. solutions moving through the extreme points of the multifunction). Then for the Dirichlet problem we show that the extremal solutions are dense in the C 1 ( T , R N ) -norm in the set of solutions of the “convex” problem (relaxation theorem).

Topological properties of the solution set of integrodifferential inclusions

Evgenios P. Avgerinos, Nikolaos S. Papageorgiou (1995)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

In this paper we examine nonlinear integrodifferential inclusions in ℝ N . For the nonconvex problem, we show that the solution set is a retract of the Sobolev space W 1 , 1 ( T , ℝ N ) and the retraction can be chosen to depend continuously on a parameter λ . Using that result we show that the solution multifunction admits a continuous selector. For the convex problem we show that the solution set is a retract of C ( T , ℝ N ) . Finally we prove some continuous dependence results.