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Abstract inclusions in Banach spaces with boundary conditions of periodic type

100%

Guedda L., Hallouz A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 2

229-253

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ $x ∈ S(x(0), sel_{F}(x))$ ⎨ ⎩ x (T) = x(0), where, $F:[0,T] × 𝓚 → 2^E \∅$ is a multivalued map with convex compact values, 𝓚 ⊂ E, $sel_{F}$ is the superposition operator generated by F, and S: 𝓚 × L¹([0,T];E) → C([0,T]; 𝓚 ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive operators generating not necessarily a compact semigroups.

On nonlinear, nonconvex evolution inclusions

100%

Papageorgiou N.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1995

tom 15

nr 1

29-42

We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, $G_δ$-subset of the solution set of the original Cauchy problem. As an application, we obtain "bang-bang"' type theorems for two nonlinear parabolic distributed parameter control systems.

Ograniczanie wyników

2 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Guedda L.

1 Hallouz A.

1 Papageorgiou N.

1 2014

1 1995

Wyniki wyszukiwania

Abstract inclusions in Banach spaces with boundary conditions of periodic type

On nonlinear, nonconvex evolution inclusions