A nonoscillation theorem for Emden--Fowler equations.
The author proves a nonoscillation theorem for the second-order Emden-Fowler equation \[ \quad y''+a(x)| y| ^{\gamma-1}y=0, \quad \gamma>0, \tag{E} \] where \(a(x)\) is positive and absolutely continuous on \((0,\infty)\). Let \(\psi(x)=x^{(\gamma+3)/2+\delta}\) where \(\delta\) is any positive number. The following theorem is proved: Let \(\gamma \not =1\). If \(\psi(x)\) satisfies (a) \(\lim_{x\rightarrow \infty} \psi(x)=k>0\) and (b) \(\int^{\infty}| \psi'(x)|\, dx<\infty\), then equation (E) is nonoscillatory.
scientific article; zbMATH DE number 1866657