Asymptotic integration of second-order nonlinear delay differential equations

We study the asymptotic integration problem for second-order nonlinear delay differential equations of the form (p(t)x′(t))′+q(t)x(t)=f(t,x(g(t)))(p(t)x′(t))′+q(t)x(t)=f(t,x(g(t))). It is shown that if uu and vv are principal and nonprincipal solutions of equation (p(t)x′)′+q(t)x=0(p(t)x′)′+q(t)x=0, then there are solutions x1(t)x1(t) and x2(t)x2(t) of the above nonlinear equation such that x1(t)=au(t)+o(u(t)),t→∞ and x2(t)=bv(t)+o(v(t)),t→∞.