Nonlocal Problems for Differential Inclusions in Hilbert Spaces

Benedetti, Irene; Loi, Nguyen Van; Malaguti, Luisa

doi:10.1007/s11228-014-0280-9

Cited by 16 publications

(9 citation statements)

References 15 publications

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“…In [10], Cardinali et al considered the impulsive semilinear differential inclusions under the assumptions of the measure of noncompactness with multivalued perturbations F. Moreover, Byszewski and Lakshmikantham [9] introduced the nonlocal Cauchy problems as the corresponding models that can describe the phenomena more accurately than the classical initial condition u(0) = u 0 alone. Therefore, it has been studied extensively under various conditions on A and F by several authors (see [3,8,20]). We remark that the main difficulty on nonlocal Cauchy problem is how to get the compactness of the solution operator at zero.…”

Section: Introductionmentioning

confidence: 99%

Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

Ji¹

2017

J. Nonlinear Sci. Appl.

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In this paper, we study the existence of mild solutions to impulsive differential inclusions with nonlocal conditions in general Banach spaces when operator semigroup is not compact. By using measure of noncompactness and multivalued analysis, we give some sufficient conditions on the existence results where the impulsive items and the nonlocal items are compact and Lipschitz continuous, respectively. An example concerning with the partial differential equation is also presented. c 2017 all rights reserved.

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Section: Introductionmentioning

confidence: 99%

Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

Ji¹

2017

J. Nonlinear Sci. Appl.

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“…Then it has been studied extensively under various conditions, see [3,4,7,8,13,14,21]. Byszewski and Lakshmikantham [9] obtained the existence and uniqueness of mild solutions in the case that Lipschitz-type conditions are satisfied.…”

Section: Introductionmentioning

confidence: 99%

On the evolution differential inclusions under a noncompact evolution system

Min¹,

Ji²,

Wen³

2016

J. Nonlinear Sci. Appl.

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We study the existence of mild solutions to differential inclusions with nonlocal conditions. The first result is established when evolution system is equicontinuous and multifunction is upper semi-continuous. Then another result is obtained when evolution system is not equicontinuous and not compact. The measure of noncompactness and the fixed point theorem for multivalued mappings play key roles in the proof. An example is provided to illustrate our results.

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“…For example, the mathematical modeling of a variety of physical processes gives rise to periodic solutions. For this reason, existence of periodic solutions to nonlinear differential inclusions has been extensively investigated by many authors in the last decades (see [9,10,11,12,13,14,15,16,17,18]). Recently, periodic solution for (2) associated with monotone operators has received some attention (see [8,9,10,15,19,20,21]).…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions for nonlinear differential inclusions with multivalued perturbations

Qin

Xue

2015

Journal of Mathematical Analysis and Applications

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Please cite this article in press as: S. Qin, X. Xue, Periodic solutions for nonlinear differential inclusions with multivalued perturbations, AbstractIn this paper, the periodic solutions for nonlinear differential inclusion governed by convex subdifferential and different perturbations are studied. It is firstly proved that the differential inclusion has unique periodic solution, if the perturbation function is a single-valued function. Then, by Schauder's fixed point theorem and Kakutani's fixed point theorem, we prove that the differential inclusion has at least a periodic solution, when the perturbation function is a upper semicontinous (or lower semicontinous) multifunction. Moreover, the existence of the extremal solution for the differential inclusion is also studied. Finally, based on one-sided Lipschitz (OSL) assumption, we prove the related relaxation theorem.

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Nonlocal Problems for Differential Inclusions in Hilbert Spaces

Cited by 16 publications

References 15 publications

Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

On the evolution differential inclusions under a noncompact evolution system

Periodic solutions for nonlinear differential inclusions with multivalued perturbations

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