A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integrodifferential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.
An approximation solvability method for nonlocal differential problems in Hilbert spaces / Benedetti, Irene; Loi, Nguyen V.; Malaguti, Luisa; Obukhovskii, Valeri. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - ELETTRONICO. - 19:2(2017), pp. 1-33. [10.1142/S0219199716500024]
An approximation solvability method for nonlocal differential problems in Hilbert spaces
MALAGUTI, Luisa
;
2017
Abstract
A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integrodifferential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.File | Dimensione | Formato | |
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