NONTRIVIAL SOLUTIONS FOR THE NONLINEAR BIHARMONIC SYSTEM WITH DIRICHLET BOUNDARY CONDITION

Abstract

We investigate the existence of multiple nontrivial so-
lutions (ξ, η) for perturbations g1 , g2 of the harmonic system with
Dirichlet boundary condition
∆^2 ξ + c∆ξ = g1 (2ξ + 3η) in Ω,
∆ η + c∆η = g2 (2ξ + 3η) in Ω,
where we assume that λ1 < c < λ2 , g1' (∞), g2' (∞) are finite. We
prove that the system has at least three solutions under some con-
dition on g.