Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method
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...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/2258546 |
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| _version_ | 1849396582826377216 |
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| author | Droh Arsène Béhi Assohoun Adjé Konan Charles Etienne Goli |
| author_facet | Droh Arsène Béhi Assohoun Adjé Konan Charles Etienne Goli |
| author_sort | Droh Arsène Béhi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b1d143e389bd45dca129e49d54ac5e8a |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b1d143e389bd45dca129e49d54ac5e8a2025-08-20T03:39:18ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/2258546Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions MethodDroh Arsène Béhi0Assohoun Adjé1Konan Charles Etienne Goli2Université de ManUniversité Félix Houphouët BoignyEcole Supérieure Africaine de Technologies de l’Information et de la Communication (ESATIC)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.http://dx.doi.org/10.1155/2024/2258546 |
| spellingShingle | Droh Arsène Béhi Assohoun Adjé Konan Charles Etienne Goli Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method Journal of Mathematics |
| title | Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method |
| title_full | Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method |
| title_fullStr | Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method |
| title_full_unstemmed | Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method |
| title_short | Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method |
| title_sort | study of nonlinear second order differential inclusion driven by a φ laplacian operator using the lower and upper solutions method |
| url | http://dx.doi.org/10.1155/2024/2258546 |
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