On the existence of monotone positive solutions of second order differential equations (Q1682379)

The author investigates the existence of positive global solutions of the nonlinear boundary value problem \[ \begin{aligned} (px')'+q(t)x &=f(t,x),\\ x(t_0)& =0,\\ x(t)& =cv(t)+\sigma (u(t)) \text{ as } t\to \infty, \end{aligned} \] where \(p\in C([t_0, \infty), [0, \infty))\), \(q\in C([t_0, \infty), R)\), \(f\in C([t_0, \infty)\times \mathbb R, \mathbb R)\), \(v(t)\) is nonprincipal solution of the equation \((px')'+q(t)x=0\).