Oscillation and nonoscillation of two terms linear and half-linear equations of higher order.
This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.
Our purpose is to analyze a first order nonlinear differential equation with advanced arguments. Then, some sufficient conditions for the oscillatory solutions of this equation are presented. Our results essentially improve two conditions in the paper “Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments” by N. Kilıç, Ö. Öcalan and U. M. Özkan. Also we give an example to illustrate our results.
Oscillation criteria are obtained for nonlinear homogeneous third order differential equations of the form and y”’ + q(t)y’ + p(t)f(y) = 0, where p and q are real-valued continuous functions on [a,∞), f is a real-valued continuous function on (-∞, ∞) and α > 0 is a quotient of odd integers. Sign restrictions are imposed on p(t) and q(t). These results generalize some of the results obtained earlier in this direction.
2000 Mathematics Subject Classification: 34K15.This paper is concerned with the oscillatory behavior of first-order delay differential equation of the form x'(t) + p(t)x (τ(t)) = 0.