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
\(c\ge 0\) 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.