• Title/Summary/Keyword: differential inclusions

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NONLOCAL FRACTIONAL DIFFERENTIAL INCLUSIONS WITH IMPULSE EFFECTS AND DELAY

  • ALSARORI, NAWAL A.;GHADLE, KIRTIWANT P.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.24 no.2
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    • pp.229-242
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    • 2020
  • Functional fractional differential inclusions with impulse effects in general Banach spaces are studied. We discuss the situation when the semigroup generated by the linear part is equicontinuous and the multifunction is Caratheodory. First, we define the PC-mild solutions for functional fractional semilinear impulsive differential inclusions. We then prove the existence of PC-mild solutions for such inclusions by using the fixed point theorem, multivalued properties and applications of NCHM (noncompactness Hausdorff measure). Eventually, we enhance the acquired results by giving an example.

CONTROLLABILITY OF IMPULSIVE FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH INFINITE DELAY IN BANACH SPACES

  • Chang, Yong-Kui
    • Journal of applied mathematics & informatics
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    • v.25 no.1_2
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    • pp.137-154
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    • 2007
  • In this paper, we establish a sufficient condition for the controllability of the first-order impulsive functional differential inclusions with infinite delay in Banach spaces. The approach used is the nonlinear alternative of Leray-Schauder type for multivalued maps. An example is also given to illustrate our result.

Second Order Impulsive Neutral Functional Differential Inclusions

  • Liu, Yicheng;Li, Zhixiang
    • Kyungpook Mathematical Journal
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    • v.48 no.1
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    • pp.1-14
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    • 2008
  • In this paper, we investigate the existence of solutions of second order impulsive neutral functional differential inclusions which the nonlinearity F admits convex and non-convex values. Some results under weaker conditions are presented. Our results extend previous ones. The methods rely on a fixed point theorem for condensing multivalued maps and Schaefer's fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values.

NONLINEAR DIFFERENTIAL INCLUSIONS OF SEMIMONOTONE AND CONDENSING TYPE IN HILBERT SPACES

  • Abedi, Hossein;Jahanipur, Ruhollah
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.2
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    • pp.421-438
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    • 2015
  • In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

SOLVABILITY OF IMPULSIVE NEUTRAL FUNCTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS WITH STATE DEPENDENT DELAY

  • Karthikeyan, K.;Anguraj, A.
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.57-69
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    • 2012
  • In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.

First Order Differential Subordinations for Carathéodory Functions

  • Gandhi, Shweta;Kumar, Sushil;Ravichandran, V.
    • Kyungpook Mathematical Journal
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    • v.58 no.2
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    • pp.257-270
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    • 2018
  • The well-known theory of differential subordination developed by Miller and Mocanu is applied to obtain several inclusions between $Carath{\acute{e}}odory$ functions and starlike functions. These inclusions provide sufficient conditions for normalized analytic functions to belong to certain class of Ma-Minda starlike functions.

EXISTENCE AND CONTROLLABILITY RESULTS FOR NONDENSELY DEFINED STOCHASTIC EVOLUTION DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS

  • Ni, Jinbo;Xu, Feng;Gao, Juan
    • Journal of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.41-59
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    • 2013
  • In this paper, we investigate the existence and controllability results for a class of abstract stochastic evolution differential inclusions with nonlocal conditions where the linear part is nondensely defined and satisfies the Hille-Yosida condition. The results are obtained by using integrated semigroup theory and a fixed point theorem for condensing map due to Martelli.