A NOTE ON THE OSCILLATION CRITERIA OF SOLUTIONS TO SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

A NOTE ON THE OSCILLATION CRITERIA OF SOLUTIONS TO SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION

Consider a solution y(t) of the nonlinear equation (E) y" ＋ f(t, y) = 0. A solution y(t) is said to be oscillatory if for every T ＞ 0 there exists $t_{0}$ ＞ T such that y($t_{0}$) = 0. Let F be the class of solutions of (E) which are indefinitely continuable to the right, i.e. y $\in$ F implies y(t) exists as a solution to (E) on some interval of the form [t$\sub$y/, $\infty$). Equation (E) is said to be oscillatory if each solution from F is oscillatory.(omitted)

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