Publicação
Existence Results for Quasilinear Elliptic Equations with Multivalued Nonlinear Terms
| Resumo: | In this paper we study the existence of solutions u ∈ W1,p0(Ω) with △pu ∈ L2(Ω) for the Dirichlet problem {−△pu(x)∈−∂Φ(u(x))+G(x,u(x)),x∈Ω,u∣∂Ω=0, (1) where Ω ⊆ RN is a bounded open set with boundary ∂Ω, △p stands for the p−Laplace differential operator, ∂Φ denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function Φ and G : Ω × R → 2R is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map u ↦ G(x, u) is upper semicontinuous with closed convex values and the second one deals with the case when u ↦ G(x, u) is lower semicontinuous with closed (not necessarily convex) values. |
|---|---|
| Autores principais: | Otani, Mitsuharu |
| Outros Autores: | Staicu, Vasile |
| Assunto: | Strong solutions Quasilinear elliptic equations Multivalued pertur Subdifferential operator |
| Ano: | 2014 |
| 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 study the existence of solutions u ∈ W1,p0(Ω) with △pu ∈ L2(Ω) for the Dirichlet problem {−△pu(x)∈−∂Φ(u(x))+G(x,u(x)),x∈Ω,u∣∂Ω=0, (1) where Ω ⊆ RN is a bounded open set with boundary ∂Ω, △p stands for the p−Laplace differential operator, ∂Φ denotes the subdifferential (in the sense of convex analysis) of a proper convex and lower semicontinuous function Φ and G : Ω × R → 2R is a multivalued map. We prove two existence results: the first one deals with the case where the multivalued map u ↦ G(x, u) is upper semicontinuous with closed convex values and the second one deals with the case when u ↦ G(x, u) is lower semicontinuous with closed (not necessarily convex) values. |
|---|