Second-order Nonlinear Differential Equations Is Always Positive Solution

In this paper, we consider the second order nonlinear functional differential equation and the nonlinear neutral functional differential equationwhere a(t) > 0 is continuous; f(t,x) is continuous and satisfies f(t,x)x > 0 for x=0; g(t) is continuous, increasing and satisfies g(t) < t, lim g(t) =∞. By introducing weighted norm and using the Banach contraction mapping principle we obtain the existence of throughout positive solutions for the above equations.