Special Session 50: Evolution equations and inclusions with applications to control, mathematical modeling and mechanics
Contents
We consider a fractional semilinear evolution inclusion in a reflexive Banach space in the presence of impulse effects associated with a very general multivalued boundary condition including several nonlocal conditions as well as the attainability problem. We assume the regularities on the nonlinear terms by means of the weak topology. Thus no compactness is assumed, neither on the evolution operator generated by the linear part, or on the nonlinear term. This technique allows to consider both sublinear and superlinear growth condition on the nonlinear term. The existence of a solution is investigated by means of a fixed point technique. The talk ends with some applications to hyperbolic integro-differential equations arising from physics and biology.