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 Second-Order Boundary Value Problem with Integral Boundary Conditions | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 260309 9 pages doi 2011 260309 Research Article Second-Order Boundary Value Problem with Integral Boundary Conditions Mouffak Benchohra 1 Juan J. Nieto 2 and Abdelghani Ouahab1 1 Department of Mathematics University ofSidi Bel Abbes BP 89 2000 Sidi Bel Abbe Algeria 2 Departamento de Analisis Matemdtico Facultad de Matemdticas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain Correspondence should be addressed to Mouffak Benchohra benchohra@ Received 28 May 2010 Revised 1 August 2010 Accepted 1 October 2010 Academic Editor Gennaro Infante Copyright 2011 Mouffak Benchohra 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. The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second-order differential equations with integral boundary conditions. The compactness of solutions set is also investigated. 1. Introduction This paper is concerned with the existence of solutions for the second-order boundary value problem -y ự f i y t a-e-1 0 1 y 0 y 1 f g s y s ds 0 where f 0 1 X R R is a given function and g 0 1 R is an integrable function. Boundary value problems with integral boundary conditions constitute a very interesting and important class of problems. They include two three multipoint and nonlocal boundary value problems as special cases. For boundary value problems with integral boundary conditions and comments on their importance we refer the reader to the papers 1-9 and the references therein. Moreover boundary value problems with integral boundary conditions have been studied by a number of authors for example 10-14 . The goal of this paper is to give existence and uniqueness results for
