An abstract Cauchy problem for higher order functional differential inclusions with infinite delay

Tran Dinh Ke; Valeri Obukhovskii; Ngai-Ching Wong; Jen-Chih Yao

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2011)

  • Volume: 31, Issue: 2, page 199-229
  • ISSN: 1509-9407

Abstract

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The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.

How to cite

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Tran Dinh Ke, et al. "An abstract Cauchy problem for higher order functional differential inclusions with infinite delay." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 31.2 (2011): 199-229. <http://eudml.org/doc/271167>.

@article{TranDinhKe2011,
abstract = {The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.},
author = {Tran Dinh Ke, Valeri Obukhovskii, Ngai-Ching Wong, Jen-Chih Yao},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Cauchy problem; functional differential inclusion; infinite delay; higher order; existence family; phase space; fixed point; multivalued map; measure of noncompactness; condensing map; multi-valued map},
language = {eng},
number = {2},
pages = {199-229},
title = {An abstract Cauchy problem for higher order functional differential inclusions with infinite delay},
url = {http://eudml.org/doc/271167},
volume = {31},
year = {2011},
}

TY - JOUR
AU - Tran Dinh Ke
AU - Valeri Obukhovskii
AU - Ngai-Ching Wong
AU - Jen-Chih Yao
TI - An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2011
VL - 31
IS - 2
SP - 199
EP - 229
AB - The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
LA - eng
KW - Cauchy problem; functional differential inclusion; infinite delay; higher order; existence family; phase space; fixed point; multivalued map; measure of noncompactness; condensing map; multi-valued map
UR - http://eudml.org/doc/271167
ER -

References

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