Publicação
The method of upper-lower solutions for nonlinear second order differential inclusions
| Resumo: | In this paper we consider a second order differential inclusion driven by the ordinary p-Laplacian, with a subdifferential term, a discontinuous perturbation and nonlinear boundary value conditions. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions φ and ψ respectively, using truncations and penalization techniques and results from nonlinear and multivalued analysis, we prove the existence of solutions in the order interval [ψ,φ] and of extremal solutions in [ψ,φ]. We show that our problem incorporates the Dirichlet, Neumann and Sturm–Liouville problems. Moreover, we show that our method of proof also applies to the periodic problem. |
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| Autores principais: | Papageorgiou, Nikolaos |
| Outros Autores: | Staicu, Vasile |
| Assunto: | Upper and lower solutions Extremal solutions Truncation and penalty functions Multifunctions Fixed points |
| Ano: | 2007 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| Resumo: | In this paper we consider a second order differential inclusion driven by the ordinary p-Laplacian, with a subdifferential term, a discontinuous perturbation and nonlinear boundary value conditions. Assuming the existence of an ordered pair of appropriately defined upper and lower solutions φ and ψ respectively, using truncations and penalization techniques and results from nonlinear and multivalued analysis, we prove the existence of solutions in the order interval [ψ,φ] and of extremal solutions in [ψ,φ]. We show that our problem incorporates the Dirichlet, Neumann and Sturm–Liouville problems. Moreover, we show that our method of proof also applies to the periodic problem. |
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