OSCILLATION OF SOLUTIONS TO SECOND-ORDER NONLINEAR DIFFERENTIAL EQUATIONS

A solution y(t) of (1) y″ + f(t, y) = 0 is said to be oscillatory if for every T > 0 there exists t0 > T such that y(t0) = 0. Let F be the class ofsolutions of (1) which are indefinitely continuable to the right, i.e. y∈F implies y(t)exists as a solution to (1) on some interval ofthe form [Ty, ∞).Equation (1)is said to be oscillatory if each solution fromF is oscillatory. If no solution in F is oscillatory, equation (1) is said to be nonoscillatory. © 1968 by Pacific Journal of Mathematics.