Semilinear systems with a multi-valued nonlinear term

In-Sook Kim, and Suk-Joon Hong. "Semilinear systems with a multi-valued nonlinear term." Open Mathematics 15.1 (2017): 628-644. <http://eudml.org/doc/288450>.

@article{In2017,
abstract = {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.},
author = {In-Sook Kim, Suk-Joon Hong},
journal = {Open Mathematics},
keywords = {Semilinear system; Multi-valued operator; Operators of monotone type; Degree theory},
language = {eng},
number = {1},
pages = {628-644},
title = {Semilinear systems with a multi-valued nonlinear term},
url = {http://eudml.org/doc/288450},
volume = {15},
year = {2017},
}

TY - JOUR
AU - In-Sook Kim
AU - Suk-Joon Hong
TI - Semilinear systems with a multi-valued nonlinear term
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 628
EP - 644
AB - 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.
LA - eng
KW - Semilinear system; Multi-valued operator; Operators of monotone type; Degree theory
UR - http://eudml.org/doc/288450
ER -