Artículos de revistas
Positive solutions to a fourth-order elliptic problem by the Lusternik-Schnirelmann category
Fecha
2014-12-01Registro en:
Journal of Mathematical Analysis and Applications, San Diego, v.420, n.1, p.532-550, 2014
0022-247X
10.1016/j.jmaa.2014.05.084
Autor
Melo, Jéssyca Lange Ferreira
Santos, Ederson Moreira dos
Institución
Resumen
In this paper we consider the fourth-order problem [...] where Ω is a smooth bounded domain in 'R POT.N', N ≥ 5 and '2 IND.∗" = 2N/(N − 4). We assume 2 ≤ s + 1 < '2 IND.∗' in case N ≥ 8 and '2 IND.∗' − 2 < s + 1 < '2 IND.∗' for the critical dimensions N = 5, 6, 7. Then we prove that if Ω has a rich topology, described by its Lusternik Schnirelmann category, then the problem has multiple solutions, at least as many as catΩ(Ω), in case the parameter μ > 0 is sufficiently small.