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Approximate weak invariance for semilinear differential inclusions in Banach spaces

100%
Lazu A., Postolache V.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1143-1155
EN
In this paper we give a criterion for a given set K in Banach space to be approximately weakly invariant with respect to the differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A generates a C 0-semigroup and F is a given multi-function, using the concept of a tangent set to another set. As an application, we establish the relation between approximate solutions to the considered differential inclusion and solutions to the relaxed one, i.e., x′(t) ∈ Ax(t) + $\overline {co} $ F(x(t)), without any Lipschitz conditions on the multi-function F.
2
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Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

64%
Olszowy L.
Open Mathematics
|
2014
|
tom 12
|
nr 4
623-635
EN
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
3
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Existence results for fractional integro-differential inclusions with state-dependent delay

64%
Siracusa G., Henríquez H. R., Cuevas C.
Nonautonomous Dynamical Systems
|
2017
|
tom 4
|
nr 1
62-77
EN
In this paper we are concerned with a class of abstract fractional integro-differential inclusions with infinite state-dependent delay. Our approach is based on the existence of a resolvent operator for the homogeneous equation.We establish the existence of mild solutions using both contractive maps and condensing maps. Finally, an application to the theory of heat conduction in materials with memory is given.
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