In this talk we present a new fixed point theorem for multimaps condensing with respect to a vectorial measure of noncompactness in a Banach space. Then, by using a $I\!\!R^2$-valued measure of noncompactness involving a Volterra integral operator, we prove the existence of mild solutions for problems governed by semilinear integro-differential inclusions, We point out that our vectorial measure of noncompactness leads us to study integro-differential problems by means of topological methods. We conclude this presentation with an application to a biological model described by a partial differential equation of reaction-diffusion type involving a distributed time delay.
An application of topological methods in problems involving semilinear integro-differential inclusions
RUBBIONI, Paola;CARDINALI, Tiziana
2015
Abstract
In this talk we present a new fixed point theorem for multimaps condensing with respect to a vectorial measure of noncompactness in a Banach space. Then, by using a $I\!\!R^2$-valued measure of noncompactness involving a Volterra integral operator, we prove the existence of mild solutions for problems governed by semilinear integro-differential inclusions, We point out that our vectorial measure of noncompactness leads us to study integro-differential problems by means of topological methods. We conclude this presentation with an application to a biological model described by a partial differential equation of reaction-diffusion type involving a distributed time delay.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
