Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t)f (u) = 0, t∈ (0, 1), u(0) = u(1) = 0, where a ∈ C([0, 1], (0,∞)) and f :R→R is continuous and satisfies f (s)s >0 for s = 0.We establish existence and multiplicity results for nodal solutions to the problems if either f0 = 0, f∞=∞ or f0 =∞, f∞ = 0, where f (s)/s approaches f0 and f∞ as s approaches 0 and ∞, respectively. We use bifurcation techniques to prove our main results.  2004 Elsevier Inc. All rights reserved