Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line (Q1412631)

The authors consider the following singular boundary value problem for a second-order differential equation on the half-line \[ {1\over p(t)} (p(t)x'(t))'+ f(t, x(t))= 0,\quad t\in (0,+\infty), \] \(x(0)= 0\), \(\lim_{t\to+\infty} p(t) x'(t)= b> 0\), where \(p\in C([0,+\infty), \mathbb R)\cap C'(0,\infty)\), \(p(t)> 0\) for \(t\in (0,\infty)\), and \(f\in C(0,\infty)\times (0,\infty))\). They show that under certain additional conditions imposed on the functions \(p\) and \(f\), the above problem has at least two nonnegative unbounded solutions.