Existence of solution for a class of quasilinear elliptic problem without Delta(2)-condition

Autor(es)

Alves, Claudianor O. ^[1] ; Silva, Edcarlos D. ^[2] ; Pimento, Marcos T. O. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Campina Grande, Unidade Acad Matemat, BR-58429970 Campina Grande, PB - Brazil

^[2] Univ Fed Goias, Int Matemat & Estat, BR-74001970 Goiania, Go - Brazil

^[3] Univ Estadual Paulista, Dept Matemat & Comp, Fac Ciencias & Tecnol, UNESP, BR-19060900 Presidente Prudente, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: ANALYSIS AND APPLICATIONS; v. 17, n. 4, p. 665-688, JUL 2019.
• Citações Web of Science: 0

Resumo

The existence and multiplicity of solutions for a class of quasilinear elliptic problems are established for the type [ -Delta phi u = f (u) in Omega u = 0 on partial derivative Omega where Omega subset of R-N, N >= 2, is a smooth bounded domain. The nonlinear term f : R -> R is a continuous function which is superlinear at the origin and infinity. The function phi : R -> R is an N-function where the well-known Delta(2)-condition is not assumed. Then the Orlicz-Sobolev space phi(t) = (e(t2) - 1)/2, t >= 0. Here, we consider some situations where it is possible to work with global minimization, local minimization and mountain pass theorem. However, some estimates employed here are not standard for this type of problem taking into account the modular given by the N-function phi. (AU)

• Processo FAPESP: 17/01756-2 - Métodos variacionais aplicados a problemas modelados no espaço das funções de variação limitada
• Beneficiário: Marcos Tadeu de Oliveira Pimenta
• Modalidade de apoio: Auxílio à Pesquisa - Regular