Solvability of inclusions of Hammerstein type
Functional Analysis
2019-03-20 v2 Classical Analysis and ODEs
Abstract
A fairly general continuation theorem of Leray-Schauder type for the class of so-called admissible multimaps is set forth. This result is then used to establish a universal rule for solving operator inclusions of Hammerstein type in Lebesgue-Bochner spaces. Examples illustrating the legitimacy of this approach include the initial value problem for perturbation of -accretive mutivalued differential equations, the anti-periodic problem for semilinear differential inclusions, abstract integral inclusions of Fredholm and Volterra type and the two-point boundary value problem for nonlinear evolution inclusions.
Keywords
Cite
@article{arxiv.1901.01112,
title = {Solvability of inclusions of Hammerstein type},
author = {Radosław Pietkun},
journal= {arXiv preprint arXiv:1901.01112},
year = {2019}
}