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" The set of solutions to a nonlinear integrodifferential equation in N variables"

In this paper, we study the existence and the compactness of the set of solutions for a nonlinear integrodifferential equation in N variables. The main tools are the fixed point theorem of Krasnosel’skii with the definition of a suitable Banach space and a sufficient condition for relative compactness of subsets in this space. An illustrative example is given.