Existence and Multiplicity Results for Second-Order Nonlinear Differential Equations with Multivalued Boundary Conditions - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.6, June 2019

Existence and Multiplicity Results for Second-Order Nonlinear Differential Equations with Multivalued Boundary Conditions ()

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DOI: 10.4236/jamp.2019.76091 759 Downloads 1,569 Views

Author(s)

Droh Arsene Behi, Assohoun Adje

Affiliation(s)

Faculty of Mathematics and Computer Science, Felix Houphouet Boigny University, Cocody Abidjan, Ivory Coast.

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.

KEYWORDS

Φ-Laplacian, Lower and Upper Solutions, Maximal Monotone Maps, Bernstein-Nagumo-Wintner Growth Condition, Leray-Schauder Topological Degree

Share and Cite:

Behi, D. and Adje, A. (2019) Existence and Multiplicity Results for Second-Order Nonlinear Differential Equations with Multivalued Boundary Conditions. Journal of Applied Mathematics and Physics, 7, 1340-1368. doi: 10.4236/jamp.2019.76091.

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