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— Si mostra come la scelta di una topologia nello spazio delle funzioni ammissibili, in taluni problemi, influenzi i relativi risultati. Vengono mostrati tre esempi. Due tratti dall'Analisi matematica pura: uno riguardante la stabilità della soluzione di un'equazione integrale di Volterra e l'altro il problema di Cauchy per l'equazione di Laplace come «problema ben posto». Il terzo esempio è relativo alla Fisica matematica, precisamente al «Principio della Memoria evanescente» in Viscoelasticità....
We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral systems...
This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.
In this paper we study the resolution problem of an integral equation with operator valued kernel. We prove the equivalence between this equation and certain time varying linear operator system. Sufficient conditions for solving the problem and explicit expressions of the solutions are given.
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