Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and N is a nonlinear multi-valued operator of monotone type. Using the nonresonance result, we next show that abstract semilinear system has a solution under certain conditions on N = (N1, N2), provided that L = (L1, L2) satisfies dim Ker L1 = ∞ and dim Ker L2 < ∞. As an application, periodic Dirichlet problems for the system involving the wave operator and a discontinuous nonlinear term are discussed.
@article{bwmeta1.element.doi-10_1515_math-2017-0056,
author = {In-Sook Kim and Suk-Joon Hong},
title = {Semilinear systems with a multi-valued nonlinear term},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {628-644},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0056}
}
In-Sook Kim; Suk-Joon Hong. Semilinear systems with a multi-valued nonlinear term. Open Mathematics, Tome 15 (2017) pp. 628-644. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0056/