Monotone positive solutions for a class of second-order nonlinear differential equations

It is shown that the second-order nonlinear differential equation (p(t)x′)′+q(t)x=f(t,x,x′),t≥0 has monotone positive solutions asymptotic to a prescribed nonprincipal solution v(t) at ∞ of the corresponding linear homogeneous equation (p(t)x′)′+q(t)x=0,t≥0, where p∈C([0,∞),(0,∞)), q∈C([0,∞),R) and f∈C([0,∞)×R×R,R).An example is given to illustrate the obtained result.