TAILIEUCHUNG - Báo cáo sinh học: " Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 654871 26 pages doi 2011 654871 Research Article Multiple Positive Solutions of Fourth-Order Impulsive Differential Equations with Integral Boundary Conditions and One-Dimensional p-Laplacian Meiqiang Feng School of Applied Science Beijing Information Science Technology University Beijing 100192 China Correspondence should be addressed to Meiqiang Feng meiqiangfeng@ Received 2 February 2010 Revised 25 April 2010 Accepted 5 June 2010 Academic Editor Gennaro Infante Copyright 2011 Meiqiang Feng. 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. By using the fixed point theory for completely continuous operator this paper investigates the existence of positive solutions for a class of fourth-order impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian. Moreover we offer some interesting discussion of the associated boundary value problems. Upper and lower bounds for these positive solutions also are given so our work is new. 1. Introduction The theory of impulsive differential equations describes processes which experience a sudden change of their state at certain moments. Processes with such a character arise naturally and often especially in phenomena studied in physics chemical technology population dynamics biotechnology and economics. For an introduction of the basic theory of impulsive differential equations see Lakshmikantham et al. 1 for an overview of existing results and of recent research areas of impulsive differential equations see Benchohra et al. 2 . The theory of impulsive differential equations has become an important area of investigation in recent years and is much richer than the corresponding theory of differential equations see . 3-18 and references

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