Oscillation and nonoscillation of nonhomogeneous third order differential equations
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.
Criteria for oscillatory behavior of solutions of fourth order half-linear differential equations of the form where is a constant and is positive continuous function on , are given in terms of an increasing continuously differentiable function from to which satisfies .