In this note we show the existence of mild solutions to a nonlocal semilinear integro-differential problem via a new $erre^2$-valued measure of noncompactness involving a Volterra integral operator. Our existence result extends in a broad sense some recent theorems for integro-differential equations. Then we provide a compactness result on the mild solution set and an application to a reaction-diffusion problem involving a distributed time delay.
Nonlocal semilinear integro-differential inclusions via vectorial measures of noncompactness
CARDINALI, Tiziana;RUBBIONI, Paola
2017
Abstract
In this note we show the existence of mild solutions to a nonlocal semilinear integro-differential problem via a new $erre^2$-valued measure of noncompactness involving a Volterra integral operator. Our existence result extends in a broad sense some recent theorems for integro-differential equations. Then we provide a compactness result on the mild solution set and an application to a reaction-diffusion problem involving a distributed time delay.File in questo prodotto:
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