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báo cáo hóa học:" Research Article On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for "

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 On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 808124 14 pages doi 10.1155 2009 808124 Research Article On Some Generalizations Bellman-Bihari Result for Integro-Functional Inequalities for Discontinuous Functions and Their Applications Angela Gallo1 and Anna Maria Piccirillo2 1 Department of Mathematics and Applications R.Caccioppoli University of Naples Federico II Claudio street 21 80125 Naples Italy 2 Department of Civil Engineering Second University of Naples Roma street 21 81100 Caserta Italy Correspondence should be addressed to Angela Gallo angallo@unina.it Received 22 December 2008 Revised 21 April 2009 Accepted 28 May 2009 Recommended by Juan J. Nieto We present some new nonlinear integral inequalities Bellman-Bihari type with delay for discontinuous functions integro-sum inequalities impulse integral inequalities . Some applications of the results are included conditions of boundedness uniformly stability by Lyapunov uniformly practical stability by Chetaev uniformly for the solutions of impulsive differential and integrodifferential systems of ordinary differential equations. Copyright 2009 A. Gallo and A. M. Piccirillo. 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. 1. Introduction The first generalizations of the Bihari result for discontinuous functions which satisfy nonlinear impulse inequality integro-sum inequality are connected with such types of inequalities a vft c f p r vm r dT pi v ti - 0 m 0 m Ỷ1 1.1 t0 ÌQ ti t b t v t c p r v r dr piV ti - 0 1.2 t0 t 0 ti t 2 Boundary Value Problems Which are studied in the publications by Bainov Borysenko lovane Laksmikantham Leela Martynyuk Mitropolskiy Samoilenko 1-13 and in many others. In these investigations the method of integral inequalities for continuous functions is generalized to the case of piecewise .