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

Abstract

We are concerned with semilinear biharmonic equations of the form where B denotes the unit ball in ℝ N , N ≥ 1, λ > 0 is a parameter, ∂/∂ν is the outward normal derivative, f : ℝ → (0, +∞) is a continuous function that has super-linear growth at infinity. We use bifurcation theory, combined with an approximation scheme 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 subcritical condition, we show that the branch must bifurcate from infinity at λ = 0.