Oscillation Criteria for y"" + p(t)f(y,y’) = 0 with f Homogeneous of Degree One

Abstract

Let be the class of functions f : R2 → R satisfying (1) f is continuous, (2) for all t, x, y ∈ R, (4) f is locally Lipschitzian. The classical Sturm theorems, the Leighton-Wintner oscillation theorem, and perturbation theorems have been established by Bihari in [1; 2; 3] for the equation , .This paper investigates the question of strong oscillation of(1.1)for p ∈ C[0, ∞ ), f ∈ . The equation is viewed as “almost linear” because of the homogeneity and sign conditions on f.