Infinitely Many Nodal Solutions of Superlinear Third Order Two-Point Boundary Value Problems

We are concerned with the existence of nodal solutions for a third order boundary value problem {u '''(x)=g(u(x)) +p(x, u(x), u '(x), u ''(x)), x is an element of(0, 1), u(0) =u(1) =u '(1) = 0, where g: R -> R is continuous and satisfies lim|xi| -> infinity g(xi)/xi = infinity (g is superlinear as |xi| -> infinity) p:[0, 1] x R-3 -> R is continuous and satisfies |p(x, xi(0), xi(1), xi(2))| <= C+|xi(0)|/3, x is an element of [0, 1], (xi(0), xi(1), xi(2))is an element of R-3, for some C > 0. We obtain infinitely many solutions having specified nodal properties. The proof of our main result is based upon bifurcation techniques.