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.