Khattabi, N.E., Frigon, M. and Ayyadi, N. (2013) Multiple Solutions of Boundary Value Problems with φ-Laplacian Operators and under a Wintner-Nagumo Growth Condition. Boundary Value Problems, 2013, 236.
https://doi.org/10.1186/1687-2770-2013-236

has been cited by the following article:

• 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.