TAILIEUCHUNG - báo cáo hóa học:" Research Article Existence and Uniqueness Results for Perturbed Neumann Boundary Value Problems"

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 Existence and Uniqueness Results for Perturbed Neumann Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 494210 10 pages doi 2010 494210 Research Article Existence and Uniqueness Results for Perturbed Neumann Boundary Value Problems Jieming Zhang1 and Chengbo Zhai2 1 Business College of Shanxi Universit Taiyuan Shanxi 030031 China 2 School of Mathematical Sciences Shanxi University Taiyuan Shanxi 030006 China Correspondence should be addressed to Chengbo Zhai cbzhai@ Received 20 April 2010 Accepted 28 June 2010 Academic Editor Irena Rachunkova Copyright 2010 J. Zhang and C. Zhai. 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. Using a fixed point theorem of general a-concave operators we present in this paper criteria which guarantee the existence and uniqueness of positive solutions for two classes of nonlinear perturbed Neumann boundary value problems for second-order differential equations. The theorems for Neumann boundary value problems obtained are very general. 1. Introduction and Preliminaries In this paper we are interested in the existence and uniqueness of positive solutions for the following nonlinear perturbed Neumann boundary value problems NBVPs P u f m2u t f t u ty g f 0 t 1 u 0 u 1 0 where m is a positive constant f 0 1 X 0 x 0 x and g 0 1 0 x are continuous. It is well known that Neumann boundary value problem for the ordinary differential equations and elliptic equations is an important kind of boundary value problems. During the last two decades Neumann boundary value problems have deserved the attention of many researchers 1-10 . By using-fixed point theorems in cone in 1 5 7-9 the authors discussed the existence of positive solutions for ordinary differential equation Neumann boundary value problems. 2 Boundary Value Problems Recently the authors 4 discussed second-order superlinear .

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