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

We are concerned with semilinear biharmonic equations of the form{ Delta(2)u = lambda f(u) in B,u = partial derivative u/ partial derivative nu = 0 on partial derivative B,where B denotes the unit ball in RN , N >= 1, lambda > 0 is a parameter, partial derivative/partial derivative nu is the outward normal derivative, f : R -> (0, +infinity) 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 lambda-direction. If in addition, f satisfies certain subcritical condition, we show that the branch must bifurcate from infinity at lambda = 0.