On the oscillation of nonlinear differential systems with retarded arguments
The aim of this paper is to study asymptotic properties of the third-order quasi-linear neutral functional differential equation where , and . By using Riccati transformation, we establish some sufficient conditions which ensure that every solution of () is either oscillatory or converges to zero. These results improve some known results in the literature. Two examples are given to illustrate the main results.
In this paper we shall study some oscillatory and nonoscillatory properties of solutions of a nonlinear third order differential equation, using the results and methods of the linear differential equation of the third order.
Conditions are given for a class of nonlinear ordinary differential equations , , which includes the linear equation to possess solutions with prescribed oblique asymptote that have an oscillatory pseudo-wronskian .
For an arbitrary analytic system which has a linear center at the origin we compute recursively all its Poincare-Lyapunov constants in terms of the coefficients of the system, giving an answer to the classical center problem. We also compute the coefficients of the Poincare series in terms of the same coefficients. The algorithm for these computations has an easy implementation. Our method does not need the computation of any definite or indefinite integral. We apply the algorithm to some polynomial...