An abstract topological point of view and a general averaging principle in the theory of differential inclusions

Couchouron, Jean-François; Kamenski, Mikhail

doi:10.1016/s0362-546x(99)00181-9

Cited by 17 publications

(22 citation statements)

References 11 publications

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“…Consequently Theorem 1 in [13] and a standard homotopic continuation argument in the Topological Index Theory guarantee the existence of at least a Duhamel's solutions for…”

Section: End Of Proof Of Theorem 51mentioning

confidence: 87%

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Nonlinear observers in reflexive Banach spaces

Couchouron

Ligarius

2003

ESAIM: COCV

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Abstract.On an arbitrary reflexive Banach space, we build asymptotic observers for an abstract class of nonlinear control systems with possible compact outputs. An important part of this paper is devoted to various examples, where we discuss the existence of persistent inputs which make the system observable. These results make a wide generalization to a nonlinear framework of previous works on the observation problem in infinite dimension (see [11,18,22,26,27,38,40] and other references therein).Mathematics Subject Classification. 47H020, 47H06, 93B07, 93C20, 93C25.

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“…Consequently Theorem 1 in [13] and a standard homotopic continuation argument in the Topological Index Theory guarantee the existence of at least a Duhamel's solutions for…”

Section: End Of Proof Of Theorem 51mentioning

confidence: 87%

“…We prove here our fundamental result on the Cauchy problem CP F x 0 , namely Proposition 3.1. We postpone at the end of this Section the proof of the existence result which is done in a particular case in Prüss [31] and can be derived by a standard argument from the Theorem 1 of [13].…”

Section: End Of Proof Of Theorem 51mentioning

confidence: 99%

Nonlinear observers in reflexive Banach spaces

Couchouron

Ligarius

2003

ESAIM: COCV

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“…where η is the Hausdorff MNC in the Banach space X and mod C is the modulus of continuity in C(J; X) (see [3]). …”

Section: Preliminariesmentioning

confidence: 99%

An existence theorem for a non-autonomous second order nonlocal multivalued problem

Cardinali

Gentili²

2017

Stud. Univ. Babes-Bolyai Math.

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Abstract. In this paper we prove the existence of mild solutions for a nonlocal problem governed by an abstract semilinear non-autonomous second order differential inclusion, where the non-linear part is an upper-Caratheodory semicontinuous multimap. Our existence theorem is obtained thanks to the introduction of a fundamental Cauchy operator. Finally we apply our main result to provide the controllability of a problem involving a non-autonomous wave equation.Mathematics Subject Classification (2010): 34A60, 34G25.

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“…[72]). Topological methods: general fixed point theorem based on averaging principle and its application to differential and integral inclusions (Couchouron & Kamenski [7]). …”

Section: Miscellaneous Averaging Problemsmentioning

confidence: 99%

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

Gama

Smirnov

2013

Set-Valued Var. Anal

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The averaging method is one of the most used tools to study dynamical systems. With the development of the theory of differential inclusions, a respective generalization of the averaging method followed the steps outlined in the theory of differential equations. Presently, it has been successfully applied to a wide range of problems involving differential inclusions, simplifying the study of the systems under consideration. In this work, the main development trends and methods in the application of the averaging method to the study of stability and optimality of solutions to differential inclusions are surveyed. A detailed list of references is given and some examples of applications are presented.

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An abstract topological point of view and a general averaging principle in the theory of differential inclusions

Cited by 17 publications

References 11 publications

Nonlinear observers in reflexive Banach spaces

Nonlinear observers in reflexive Banach spaces

An existence theorem for a non-autonomous second order nonlocal multivalued problem

Stability and Optimality of Solutions to Differential Inclusions via Averaging Method

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