Existence Results of Nondensely Defined Fractional Evolution Differential Inclusions

This paper deals with the existence results of integral solutions for nondensely defined fractional evolution differential inclusions. Our approach is based on integrated semigroup theory and a fixed point theorem for condensing map due to Martelli. An example is also given to illustrate our results.

Remarks on the controllability of nonlinear perturbations of Volterra integrodifferential systems

Sufficient conditions for the complete controllability of nonlinear perturbations of Volterra integrodifferential systems with implicit derivative are established. The results generalize the results of Dauer and Balachandran [9] and are obtained through the notions of condensing map and measure of noncompactness of a set.

Controllability of nonlinear neutral Volterra integrodifferential systems

Sufficient conditions for the controllability of nonlinear neutral Volterra integrodifferential systems with implicit derivative are established. The results are a generalisation of the previous results, through the notions of condensing map and measure of noncompactness of a set.

A Note on a Theorem of Ky Fan

Fan ([2, Theorem 2]) has proved the following theorem:Let K be a nonempty compact convex set in a normed linear space X. For any continuous map f from K into X, there exists a point u∈K such thatIn this note, we prove that the above theorem is true for a continuous condensing map defined on a closed ball in a Banach space. We also prove that it is true for a continuous condensing map defined on a closed convex bounded subset of a Hilbert space.