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Existence results for fractional integro-differential inclusions with state-dependent delay

Giovana Siracusa;  Hernán R. Henríquez;  Claudio Cuevas — 2017

Nonautonomous Dynamical Systems

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.

Weighted Dispersive Estimates for Solutions of the Schrödinger Equation

Cardoso, Fernando;  Cuevas, Claudio;  Vodev, Georgi — 2008

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 35L15, 35B40, 47F05. Introduction and statement of results. In the present paper we will be interested in studying the decay properties of the Schrödinger group. The authors have been supported by the agreement Brazil-France in Mathematics – Proc. 69.0014/01-5. The first two authors have also been partially supported by the CNPq-Brazil.

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