tailieunhanh - Báo cáo hóa học: "Research Article A Fourth-Order Boundary Value Problem with One-Sided Nagumo Condition"

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 A Fourth-Order Boundary Value Problem with One-Sided Nagumo Condition | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 569191 13 pages doi 2011 569191 Research Article A Fourth-Order Boundary Value Problem with One-Sided Nagumo Condition Wenjing Song1 2 and Wenjie Gao1 1 Institute of Mathematics Jilin University Changchun 130012 China 2 Institute of Applied Mathematics Jilin University of Finance and Economics Changchun 130017 China Correspondence should be addressed to Wenjing Song songwenjing1978@ Received 10 January 2011 Accepted 9 March 2011 Academic Editor I. T. Kiguradze Copyright 2011 W. Song and W. Gao. 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 aim of this paper is to study a fourth-order separated boundary value problem with the righthand side function satisfying one-sided Nagumo-type condition. By making a series of a priori estimates and applying lower and upper functions techniques and Leray-Schauder degree theory the authors obtain the existence and location result of solutions to the problem. 1. Introduction In this paper we apply the lower and upper functions method to study the fourth-order nonlinear equation 4 f f t u t uft u ff u f 0 t 1 with f 0 1 X R4 R being a continuous function. This equation can be used to model the deformations of an elastic beam and the type of boundary conditions considered depends on how the beam is supported at the two endpoints 1 2 . We consider the separated boundary conditions u 0 u 1 0 au 0J - bu 0 A cu 1 du 1 B with a b c d e R 0 x A B e R. 2 Boundary Value Problems For the fourth-order differential equation 4 f f t u t u t u t u t 0 t 1 u 0 u 1 u 0 u 1 the authors in 3 obtained the existence of solutions with the assumption that f satisfies the two-sided Nagumo-type conditions. For more related works interested readers may refer to 1-14 . The one-sided .

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