This paper is concerned with the existence of positive homoclinic solutions for the second-order differential equation
$$begin{aligned} u^{prime prime }+cu^{prime }-a(t)u+f(t,u)=0, end{aligned}$$
where
(cge 0) is a constant and the functions
a and
f are continuous and not necessarily periodic in
t. Under other suitable assumptions on
a and
f, we obtain the existence of positive homoclinic solutions in both cases sub-quadratic and super-quadratic by using critical point theorems.