Indefinite weight nonlinear problems with Neumann boundary conditions

We present a multiplicity result of positive solutions for the Neumann problem associated with a second order nonlinear differential equation of the following form u″+a(t)g(u)=0, where the weight function a(t) has indefinite sign. The only assumption we make for the nonlinear term g(u) is that its primitive G(u) presents some oscillations at infinity, expressed by the condition involving lim_G(u)/u2=0