, Volume 59, Issue 4, pp 433-454
Date: 29 Jul 2009

Oscillation criteria for differential equations of second order

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Abstract

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form $$ (r(t)y')' + q(t)y' + p(t)f(y)g(y') = 0, t \geqslant t_0 , $$ where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Communicated by Michal Fečkan
Research supported by National Board of Higher Mathematics, Department of Atomic Energy, India.