TITLE:
Existence and Multiplicity Results for Second-Order Nonlinear Differential Equations with Multivalued Boundary Conditions
AUTHORS:
Droh Arsene Behi, Assohoun Adje
KEYWORDS:
Φ-Laplacian, Lower and Upper Solutions, Maximal Monotone Maps, Bernstein-Nagumo-Wintner Growth Condition, Leray-Schauder Topological Degree
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.6,
June
30,
2019
ABSTRACT: In this paper, we consider the following second-order
nonlinear differential equations’ problem: a.e on Φ=[0, T] with a discontinuous
perturbation and multivalued boundary conditions. By combining lower and upper
solutions method, theory of monotone operators and theory of topological degree,
we show the existence of solutions of the investigated problem in two cases. At
first, α andβ are assumed
respectively an ordered pair of lower and upper solutions of the problem,
secondly α and β are assumed
respectively non ordered pair of lower and upper solutions of the problem.
Moreover, we show multiplicity results when the problem admits a pair of lower
and strict lower solutions and a pair of upper and strict upper solutions. We
also show that our method of proof stays true for a periodic problem.