We establish the existence of mild, strong, classical solutions for a class of second order abstract functional differential equations with nonlocal conditions.
We establish existence of mild solutions for the semilinear first order functional abstract Cauchy problem and we prove that the set of mild solutions of this problem is connected in the space of continuous functions.
By using the theory of strongly continuous cosine families and the properties of completely continuous maps, we study the existence of mild, strong, classical and asymptotically almost periodic solutions for a functional second order abstract Cauchy problem with nonlocal conditions.
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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