tailieunhanh - báo cáo hóa học:" Review Article A Survey on Oscillation of Impulsive Ordinary Differential Equations"

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: Review Article A Survey on Oscillation of Impulsive Ordinary Differential Equations | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 354841 52 pages doi 2010 354841 Review Article A Survey on Oscillation of Impulsive Ordinary Differential Equations Ravi P. Agarwal 1 2 Fatma Karakoc 3 and Agacik Zafer4 1 Department of Mathematical Sciences FL Institute of Technology Melbourne FL 32901 USA 2 Mathematics and Statistics Department King Fahd University of Petroleum and Minerals Dhahran 31261 Saudi Arabia 3 Department of Mathematics Faculty of Sciences Ankara University 06100 Ankara Turkey 4 Department of Mathematics Middle East Technical University 06531 Ankara Turkey Correspondence should be addressed to Ravi P. Agarwal agarwal@ Received 1 December 2009 Accepted 3 March 2010 Academic Editor Leonid Berezansky Copyright 2010 Ravi P. Agarwal et al. 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. This paper summarizes a series of results on the oscillation of impulsive ordinary differential equations. We consider linear half-linear super-half-linear and nonlinear equations. Several oscillation criteria are given. The Sturmian comparison theory for linear and half linear equations is also included. 1. Introduction Impulsive differential equations that is differential equations involving impulse effect appear as a natural description of observed evolution phenomena of several real world problems. There are many good monographs on the impulsive differential equations 16 . It is known that many biological phenomena involving thresholds bursting rhythm models in medicine and biology optimal control models in economics pharmacokinetics and frequency modulates systems do exhibit impulse effects. Let us describe the Kruger-Thiemer model 7 for drug distribution to show how impulses occur naturally. It is assumed that the drug which is administered .