Positive solutions to a linearly perturbed critical growth biharmonic problem

Abstract

(Communicated by....) Abstract. Existence and nonexistence results for positive solutions to a lin-early perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimen-sions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced. 1. Introduction. Let B ⊂ Rn (n ≥ 5) be the unit ball, 2 ∗ = 2nn−4 denote the critical Sobolev exponent for the embedding H2(B) ⊂ L2∗(B), λ ≥ 0 and d ∈ R. We consider the following fourth order elliptic problem with linearly perturbed critical growth and Steklov boundary conditions: ∆ 2u = λu+ u2