Abstract
We are here concerned with proving boundedness theorems for a general class of second order non-linear differential equations. The first part of our result mainly deals with generalizations of the results of T. Dlotko [1], and in the second part we specialize our discussion to a more restricted subclass and prove extensions of the boundedness theorems of M. In. Leonov [2]. We first consider the following general second order non-linear differential equation: a(t) u'" ~b(t) g(u, u') + c(t) ](u) -~ e(t) (1) under the following assumptions: (A1) g(x, y) is continuous in both x and y and there exists a positive constant k such that y g(x, y) > ky 2 for all x and y, (A2) a(t), b(t) and c(t) are continuous and non-negative, and
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