Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems

We consider the fourth-order two-point boundary value problem u(m) + Mu = lambda h(t)f(u), 0 < t < 1, u(0) = u(1) = u'(0) = u'(1) = 0, where lambda is an element of R is a parameter, M is an element of (-pi(4), pi(4)/64) is given constant, h is an element of C[0,1], [0,infinity)) with h(t)not equivalent to 0 on any subinterval of [0,1], f is an element of C(R, R) satisfies f(u)u > 0 for all u not equal 0, and lim(u ->infinity) f(u)/u = 0, lim(u ->+infinity 8)f(u)/u = f(+infinity), lim(u -> 0)f(u)/u = f(0) for some f(+infinity), f(0) is an element of (0, +infinity). By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem.