Positive solutions of singular Emden-Fowler type systems (Q1202229)

Let (1) \(y''=a(t)z^{-\lambda}\), \(z''=b(t)y^{-\mu}\), \(t\geq t_ 0\), be the singular Emden-Fowler type system where \(\lambda,\mu>0\) are constants and \(a\) and \(b\) are continuous functions on \([t_ 0,\infty)\). The author obtains sufficient conditions which ensure the existence of positive solutions \((y,z)\) of (1) satisfying \(\lim_{t\to\infty}y(t)=\lim_{t\to\infty}y'(t)=0\), \(\lim_{t\to\infty}z(t)=\lim_{t\to\infty}z'(t)=0\) and \(\lim_{t\to\infty}y(t)=\ell\), \(\lim_{t\to\infty}y'(t)=0\), \(\lim_{t\to\infty}z(t)=\lim_{t\to\infty}z'(t)=0\), with \(\ell>0\). A criterion for the nonexistence of these solutions is also given.