Existence of solutions for infinite systems of differential equations by densifiability techniques

Abstract

A novel technique to state the existence of solutions for certain infinite systems of differential equations is proposed. Our main tool will be the so called degree of nondensifiability, which seems to work under more general conditions than the measures of noncompactness. In fact, in our main result, the required conditions proposed for the existence of solutions of such system are more general than others required in most of the results based on such measures.