Positive solutions to a fourth-order elliptic problem by the Lusternik-Schnirelmann category

Autor(es)

Ferreira Melo, Jessyca Lange ^[1] ; dos Santos, Ederson Moreira ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat Comp, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 420, n. 1, p. 532-550, DEC 1 2014.
• Citações Web of Science: 3

Resumo

In this paper we consider the fourth-order problem [ Delta(2)u = mu|u|(s-1)u + |u| (2{*}-2)u in Omega, [ u, -Delta u > 0 in Omega, u, Delta u = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R-N, N >= 5 and 2({*}) = 2N/(N - 4). We assume 2 <= s + 1 < 2({*}) in case N >= 8 and 2({*}) - 2 < s + 1 < 2({*}) for the critical dimensions N = 5, 6, 7. Then we prove that if Omega has a rich topology, described by its Lusternik-Schnirelmann category, then the problem has multiple solutions, at least as many as cat(Omega)(Omega), in case the parameter mu > 0 is sufficiently small. (C) 2014 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/19320-7 - Sistemas de equações elípticas de tipo hamiltoniano e equações elípticas de quarta ordem
• Beneficiário: Ederson Moreira dos Santos
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 10/00603-9 - Sistemas de equações elípticas de tipo Hamiltoniano
• Beneficiário: Jessyca Lange Ferreira Melo
• Modalidade de apoio: Bolsas no Brasil - Doutorado