We consider the boundary value problem u ''(x) + g(u(x)) + p(x, u(x), u'(x)) = 0, x is an element of (0, 1), u(0) = 0, u(1) = Sigma(m-2)(i=1)alpha(i)u(eta(i)), where: (1) m >= 3, eta(i) is an element of (0, 1) and alpha(i) > 0 with A : = Sigma(m-2)(i=1) alpha(i) < 1; (2) g : R -> R is continuous and satisfies g(s) s > 0, s not equal 0, and lim(s ->infinity) g(s)/s = infinity; (3) p: [0, 1] x R(2) -> R is continuous and satisfies |p(x, u, v)| <= C + beta|u|, x is an element of [0, 1](u, v) is an element of R(2) for some C > 0 and beta is an element of (0, 1/2). We obtain infinitely many solutions having specified nodal properties by the bifurcation techniques.