The authors are concerned with the oscillatory behavior of the second-order nonlinear differential equation with a nonlinear damping term
with It is also assumed that
for some and for all Two cases are considered:
(a) is differentiable, and for some and all and
for some and for all
(b) is not necessarily differentiable, for some and all and
for some and for all Using standard integral averaging technique, several interval oscillation criteria are obtained which require information on the behavior of the coefficients in equation (b) on a sequence of intervals such that as . Unfortunately, rather specific assumptions (b1) and (b2) significantly restrict possible the applicability of the theorems.
The statement of the fundamental Lemma 1.1 should be corrected as follows: “If there exists an interval such that (1.2) holds, then, for all (1.3) is satisfied for every " instead of the incorrect formulation “If there exist an interval and a such that (1.2) holds, then (1.3) is satisfied for every " The statement of Theorem 3.1 should be corrected by adding the phrase “and there exists a such that (3.1) holds".