Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Comparison Theorems for the Third-Order Delay Trinomial Differential Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 160761 12 pages doi 2010 160761 Research Article Comparison Theorems for the Third-Order Delay Trinomial Differential Equations B. Baculíková and J. Dzurina Department of Mathematics Faculty of Electrical Engineering and Informatics Technical University of Kosice Letna 9 042 00 Kosice Slovakia Correspondence should be addressed to J. DZurina Received 11 August 2010 Accepted 1 November 2010 Academic Editor E. Thandapani Copyright 2010 B. Baculikova and J. DZurina. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The objective of this paper is to study the asymptotic properties of third-order delay trinomial differential equation y t p f y t g f y r f 0. Employing new comparison theorems we can deduce the oscillatory and asymptotic behavior of the above-mentioned equation from the oscillation of a couple of the first-order differential equations. Obtained comparison principles essentially simplify the examination of the studied equations. 1. Introduction In this paper we are concerned with the oscillation and the asymptotic behavior of the solution of the third-order delay trinomial differential equations of the form y a pawa g a y T 0 0- E In the sequel we will assume that the following conditions are satisfied i p t 0 g 0 0 ii T t t limt T t TO. By a solution of E we mean a function y t e C1 ỊTx to Tx to that satisfies E on ỊTx to . We consider only those solutions y t of E which satisfy sup y t t T 0 for all T Tx. We assume that E possesses such a solution. A solution of E is called oscillatory if it has arbitrarily large zeros on Tx to and otherwise it is called to be nonoscillatory. Equation E itself is said to be oscillatory if all its solutions are oscillatory. 2 Advances in Difference
