Existence of a Non-Oscillating solution for a Second Order Nonlinear ODE - Bharadwaj, B.V. K.; Baruah, Pallav Kumar (Communications in Mathematics and Applications, 2015)
In this paper we have considered the following nonlinear ordinary differential equation. $$y''(x) + F(x, y(x)) = 0\tag{0.1}$$ where \(F(t,x(t))\) is real valued function on \([0,\infty) \times R\), \(x\geq 0\). We have given sufficient conditions for the existence of a non oscillating solution for equation (0.1). These conditions are generalized with respect to the nonlinear function \(F\) and are in the spirit of the classical result by Atkinson [1].
Keywords: Nonlinear coupled ordinary differential equations; Fixed-point theorem; Non-oscillation