The periodic problem for semilinear differential inclusions in Banach spaces

Ralf Bader

Displaying similar documents to “The periodic problem for semilinear differential inclusions in Banach spaces”

On the semilinear multi-valued flow under constraints and the periodic problem

Ralf Bader (2000)

Commentationes Mathematicae Universitatis Carolinae

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$^{* *}$ In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a $C_{0}$ -semigroup we show the $R_{δ}$ -structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence of periodic solutions for the semilinear system. As an application the problem...

On boundary value problems for degenerate differential inclusions in Banach spaces.

Obukhovskii, Valeri, Zecca, Pietro (2003)

Abstract and Applied Analysis

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Boundary value problems for semilinear evolution inclusions: Carathéodory selections approach

Tiziana Cardinali, Lucia Santori (2011)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.

Approximate weak invariance for semilinear differential inclusions in Banach spaces

Alina Lazu, Victor Postolache (2011)

Open Mathematics

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In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + $\bar{c o}$ F(x(t)), without any Lipschitz...

Periodic solutions to retarded and partial functional differential equations.

Pavlakos, Panaiotis K., Stratis, Ioannis G. (1994)

Portugaliae Mathematica

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Boundary value problems and periodic solutions for semilinear evolution inclusions

Nikolaos S. Papageorgiou (1994)

Commentationes Mathematicae Universitatis Carolinae

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We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.