Existence and continuous dependence results for semilinear functional differential inclusions with infinite delay

Gori, Candida; Obukhovskiĭ, Valeri; Ragni, Marcello; Rubbioni, Paola

doi:10.1016/s0362-546x(01)00861-6

Cited by 22 publications

(13 citation statements)

References 6 publications

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“…The result is more general than the related results we know (see e.g. on the real line [7] and [3] and in the case of a general Banach space via Bochner integral [4]). …”

Section: U(t) = \G(ts)f(s U(s) ^ K(s T)u(t)mentioning

confidence: 52%

Global Solutions for Volterra Ordinary and Retarded Integral Equations

Satco¹

2008

Demonstratio Mathematica

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Abstract. Using a generalization of Darbo's fixed point theorem, we obtain the existence of global solutions for nonlinear Volterra-type integral equations in Banach spaces. The involved functions are supposed to be continuous only with respect to some variables, integrability or essential boundedness conditions being also imposed. Our result improves the similar result given in [10] (where uniform continuity was required), as well as those referred by the authors of the cited paper. Finally, following the same ideas, the existence of continuous solutions is proved for a Volterra-type retarded integral equation, under less restrictive assumptions than in the others related results in literature. IntroductionThe importance of Volterra-type integral equations in solving various nonlinear problems in science determined many authors to study the existence of (continuous or better) solutions (see e.g. The setting is that of a separable Banach space and the assumptions made on the operators are much weaker than those made by the previously cited 2000 Mathematics Subject Classification: 45D05, 47H10, 49K25.

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“…The result is more general than the related results we know (see e.g. on the real line [7] and [3] and in the case of a general Banach space via Bochner integral [4]). …”

Section: U(t) = \G(ts)f(s U(s) ^ K(s T)u(t)mentioning

confidence: 52%

Global Solutions for Volterra Ordinary and Retarded Integral Equations

Satco¹

2008

Demonstratio Mathematica

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“…As to the case of infinite delay, an extensive theory is developed for (1.1), where A(t) (or A(t) ≡ A) is linear. For nonlinear case, we refer the readers to [6,12,14] and [4].…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions for Nonlinear Evolution Equations With Infinite Delay

Dong¹,

Li²

2014

Bulletin of the Korean Mathematical Society

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“…Impulsive models can be found in biological dynamics due to harvest or disease. For a complete reference on impulsive differential equations and inclusions, we refer to the monograph [7], and for recent contributions in impulsive problems, we cite in this note the typical works in [1,9,14,21,23,33].…”

Section: Introductionmentioning

confidence: 99%

“…The case when A is nondensely defined has been considered by many authors recently. We are interested in the papers [1,8,19,21,34,33] that are devoted to this situation. Since A is nondensely defined, there is no semigroup generated by A on X .…”

Section: Introductionmentioning

confidence: 99%

“…2), and then {S (t)} t≥0 is a C 0 -semigroup on D(A). The hypothesis that S (t) (t > 0) is compact was used in [1,8,19,21] to get the existence results whereas in [34] and [33], this condition was weakened by assuming that S is norm-continuous for t > 0. Regarding nonlocal problems, Liu [31] pointed out that one may meet a difficulty in proving the equicontinuity of the solution operator if the Lipschitz or compactness assumption on the nonlocal function is relaxed.…”

Section: Introductionmentioning

confidence: 99%

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