We consider the existence of positive solutions for boundary value problems (p(t)u′)′+λf(t,u)=0, r<t<R;au(r)-bp(r)u′(r)=0;cu(R)+dp(R)u′(R)=0, where we allow that nonlinearity f(t,u) be negative. If f is sublinear at u=+∞ and unbounded, there exists a λ*>0, the above boundary value problems has a positive solution for every λ>λ*. |