Artigo
Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N
Registro en:
Milan Journal Of Mathematics. Basel: Springer Basel Ag, v. 82, n. 2, p. 213-231, 2014.
1424-9286
10.1007/s00032-014-0224-8
WOS:000345142800002
Autor
Bastos, Waldemar D. [UNESP]
Miyagaki, Olimpio H.
Vieira, Ronei S.
Resumen
We establish a result on the existence of a positive solution for the following class of degenerate quasilinear elliptic problems:(P) {-Delta(up)u + V(x)vertical bar x vertical bar-(ap+)vertical bar u vertical bar(p-2)u = K(x)f(x, u), in R-N, u > 0, in R-N, u epsilon D-u(1,p)(R-N),where -Delta(ap)u = -div(vertical bar x vertical bar(-ap)vertical bar del u vertical bar(p-2)del u), 1 < p < N, -infinity < a < N-p/p, a <= e <= a + 1, d = 1 + a - e, and p* := p*(a, e) = Np/N-dp denotes the Hardy-Sobolev's , and denotes the Hardy-Sobolev's critical exponent, V and K are bounded nonnegative continuous potentials, K vanishes at infinity, and f has a subcritical growth at infinity. The technique used here is the variational approach. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) Centro Federal de Educacao Tecnologica de Minas Gerais/Brazil Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Univ Estadual Paulista, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil Univ Fed Juiz de Fora, BR-36036330 Juiz De Fora, MG, Brazil Ctr Fed Educ Tecnol Minas Gerais, BR-35503822 Divinopolis, MG, Brazil Univ Estadual Paulista, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil FAPEMIG: CEX-APQ 00025-11