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

作者：Ferreira Melo Jessyca Lange; dos Santos Ederson Moreira

来源：Topological Methods in Nonlinear Analysis, 2015, 45(2): 551-574.

DOI：10.12775/tmna.2015.026

• Biharmonic equation
• Critical exponent
• Lusternik-Schnirelman category
• Positive solutions

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.

• 出版日期2015-6