Global bifurcation of positive solutions for a class of superlinear biharmonic equations

Abstract

We are concerned with semilinear biharmonic equations of the form { ∆2u = λf(u) in B,

                                                                                                                             u =∂u∂ν = 0 on ∂B,

where B denotes the unit ball in RN , N ≥ 1, λ > 0 is a parameter, ∂/∂ν is theoutward normal derivative, f : R → (0, +∞) is a continuous function that has superlinear growth at infinity. We use bifurcation theory, combined with an approximationscheme to establish the existence of an unbounded branch of positive radial solutions,which is bounded in positive λ–direction. If in addition, f satisfies certain subcriticalcondition, we show that the branch must bifurcate from infinity at λ = 0.