Conditions for the existence of nonoscillatory solutions to a second-order nonlinear differential equation (Q1582962)

The author studies the second-order nonlinear differential equation \[ y''+p(t)\|y\|\sigma\|y'\|^\lambda\sigma y=0 \tag{1} \] with \(\sigma>-1, \lambda<1,\) and \(p:[a,+\infty)\to(0,+\infty)\) is a continuous function. For \(\lambda=0\) equation (1) reduces to the well-known Emden-Fowler equation intensively studied in the literature. In the present paper, three theorems establishing nonoscillation of all regular solutions are proved.