Abstract inclusions in Banach spaces with boundary conditions of periodic type

Lahcene Guedda; Ahmed Hallouz

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2014)

  • Volume: 34, Issue: 2, page 229-253
  • ISSN: 1509-9407

Abstract

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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 ) , s e l F ( x ) ) ⎨ ⎩ x (T) = x(0), where, F : [ 0 , T ] × → 2 E is a multivalued map with convex compact values, ⊂ E, s e l F is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) 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.

How to cite

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Lahcene Guedda, and Ahmed Hallouz. "Abstract inclusions in Banach spaces with boundary conditions of periodic type." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 34.2 (2014): 229-253. <http://eudml.org/doc/270538>.

@article{LahceneGuedda2014,
abstract = {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] × → 2^E $ is a multivalued map with convex compact values, ⊂ E, $sel_\{F\}$ is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) 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.},
author = {Lahcene Guedda, Ahmed Hallouz},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {measure of noncompactness; condensing operator; nonlinear abstract inclusion; accretive operator; integral solution; nonlinear semigroup},
language = {eng},
number = {2},
pages = {229-253},
title = {Abstract inclusions in Banach spaces with boundary conditions of periodic type},
url = {http://eudml.org/doc/270538},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Lahcene Guedda
AU - Ahmed Hallouz
TI - Abstract inclusions in Banach spaces with boundary conditions of periodic type
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2014
VL - 34
IS - 2
SP - 229
EP - 253
AB - 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] × → 2^E $ is a multivalued map with convex compact values, ⊂ E, $sel_{F}$ is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) 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.
LA - eng
KW - measure of noncompactness; condensing operator; nonlinear abstract inclusion; accretive operator; integral solution; nonlinear semigroup
UR - http://eudml.org/doc/270538
ER -

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