A FOURTH-ORDER EQUATION WITH CRITICAL GROWTH: THE EFFECT OF THE DOMAIN TOPOLOGY

Author(s)

Ferreira Melo, Jessyca Lange ^[1] ; dos Santos, Ederson Moreira ^[2]

Affiliation

^[1] Univ Fed Vicosa, Dept Matemat, BR-36570000 Vicosa, MG - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 45, n. 2, p. 551-574, JUN 2015.
• Web of Science Citations: 2

Abstract

In this paper we prove the existence of multiple classical solutions for the fourth-order problem [Delta(2)u = mu u + u2{*}(-1) 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 >= 8, 2({*}) = 2N/(N - 4) and mu(1)(Omega) is the first eigenvalue of Delta(2) in H-2 (Omega) boolean AND H-0(1) (Omega). We prove that there exists 0 < <(mu)over bar> < mu(1)(Omega) such that, for each 0 < mu < <(mu)over bar>, the problem has at least cat(Omega)(Omega) solutions. (AU)

• FAPESP's process: 10/19320-7 - Hamiltonian systems of elliptic equations and fourth-order elliptic equations
• Grantee: Ederson Moreira dos Santos
• Support Opportunities: Regular Research Grants
• FAPESP's process: 10/00603-9 - Hamiltonian systems of elliptic equations
• Grantee: Jessyca Lange Ferreira Melo
• Support Opportunities: Scholarships in Brazil - Doctorate