Further results for the solutions of a third-order differential equation

Abstract

1. The equation considered here is of the formwhere a, b are constants, h(x) is differentiable and h′(x), p(t) are continuous in x, t respectively. The primary object of the paper is to prove the followingTheorem 1. Suppose that(i) a > 0,b > 0;(ii) h(0) = 0, h(x)/x ≥ δ > 0 (x ≠ 0);(iii) h′(x) ≤ c for all x where ab > c > 0.