tailieunhanh - báo cáo hóa học:" Research Article Green’s Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions ˇ Svetlana Roman and Arturas Stikonas ¯"

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 Green’s Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions ˇ Svetlana Roman and Arturas Stikonas ¯ | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 767024 23 pages doi 2011 767024 Research Article Green s Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions Svetlana Roman and Arturas Stikonas Institute of Mathematics and Informatics Vilnius University Akademijos 4 Vilnius LT-08663 Lithuania Correspondence should be addressed to Svetlana Roman Received 1 June 2010 Revised 24 July 2010 Accepted 9 November 2010 Academic Editor Gennaro Infante Copyright 2011 S. Roman and A. Stikonas. 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. We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Green s function if the general solution of a homogeneous equation is known. We have obtained the relation between two Green s functions of two nonhomogeneous problems. It allows us to find Green s function for the same equation but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions. 1. Introduction The study of boundary-value problems for linear differential equations was initiated by many authors. The formulae of Green s functions for many problems with classical boundary conditions are presented in 1 . In this book Green s functions are constructed for regular and singular boundary-value problems for ODEs the Helmholtz equation and linear nonstationary equations. The investigation of semilinear problems with Nonlocal Boundary Conditions NBCs and the existence of their positive solutions are well founded on the investigation of Green s function for linear problems with NBCs 2-7 . In