Study of Nonlinear Second-Order Differential Inclusion Driven by a ΦLaplacian Operator Using the Lower and Upper Solutions Method

Author:

Béhi Droh Arsène1ORCID,Adjé Assohoun2,Etienne Goli Konan Charles3

Affiliation:

1. Université de Man, District des Montagnes, Man, Côte d’Ivoire

2. Université Félix Houphouët Boigny, Cocody, Abidjan 22 BP 582, Côte d’Ivoire

3. Ecole Supérieure Africaine de Technologies de l’Information et de la Communication (ESATIC), Abidjan 18 BP 1501, Côte d’Ivoire

Abstract

In this paper, we study a second-order differential inclusion under boundary conditions governed by maximal monotone multivalued operators. These boundary conditions incorporate the classical Dirichlet, Neumann, and Sturm–Liouville problems. Our method of study combines the method of lower and upper solutions, the analysis of multivalued functions, and the theory of monotone operators. We show the existence of solutions when the lower solution σ and the upper solution γ are well ordered. Next, we show how our arguments of proof can be easily exploited to establish the existence of extremal solutions in the functional interval σ,γ. We also show that our method can be applied to the periodic case.

Publisher

Hindawi Limited

Reference24 articles.

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2. Mémoire sur la théorie des équations aux derivés partielles et les méthode des approximations successives;E. Picard;Journal of Pure and Applied Mathematics,1890

3. Existence and Multiplicity Results for Second-Order Nonlinear Differential Equations with Multivalued Boundary Conditions

4. Goli: lower and upper solutions method for nonlinear second-order differential equations involving a Φ-Laplacian operator;D. A. Béhi;African Diaspora Journal of Mathematics,2019

5. Multiple solutions of boundary value problems with Φ-Laplacian operators and under a Wintner-Nagumo growth condition;N. El Khattabi;Boundary Value Problems,2013

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