Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
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: UNIQUENESS OF SOLUTIONS FOR FOURTH-ORDER NONLOCAL BOUNDARY VALUE PROBLEMS | UNIQUENESS OF SOLUTIONS FOR FOURTH-ORDER NONLOCAL BOUNDARY VALUE PROBLEMS JOHNNY HENDERSON AND DING MA Received 19 January 2006 Accepted 22 January 2006 Uniqueness implies uniqueness relationships are examined among solutions of the fourth-order ordinary differential equation y 4 f x y y y y satisfying 5-point 4-point and 3-point nonlocal boundary conditions. Copyright 2006 J. Henderson and D. Ma. 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. 1. Introduction We are concerned with uniqueness of solutions of certain nonlocal boundary value problems for the fourth-order ordinary differential equation y 4 f x y y y y a x b 1.1 where A f a b X R4 R is continuous B solutions of initial value problems for 1.1 are unique and exist on all of a b . By uniqueness of solutions our meaning is uniqueness of solutions when solutions exist. In particular we deal with uniqueness implies uniqueness relationships among solutions of 1.1 satisfying nonlocal 5-point boundary conditions y x0 yt. ylx y2 y xs y3 y x4 - y xs y4 y 1 - y x2 y1 y x3 y2 y x4 y3 y xs y4 1.2 1.3 where a x1 x2 x3 x4 x5 b with solutions of 1.1 satisfying nonlocal 4-point Hindawi Publishing Corporation Boundary Value Problems Volume 2006 Article ID23875 Pages 1-12 DOI 10.1155 BVP 2006 23875 2 Fourth-order nonlocal boundary value problems boundary conditions given by y 1 y1 y xx y2 yta y3 y x3 -y x4 y4 1.4 y x1 - y xi y1 y xs y2 yta y3 y x4 y4 1.5 y x1 y1 y x2 y2 y x2 y3 y x3 -y x4 y4 1.6 y x1 - y x2 y1 y x3 y2 y x3 y3 y x4 y4 1.7 where a x1 x2 x3 x4 b as well as with solutions of 1.1 satisfying nonlocal 3-point boundary conditions given by y x1 y1 y x1 y2 y x1 y3 y x2 -y x3 y4 1.8 y x1 -y x2 y1 y x3 y2 y x3 y3 y xs y4 1.9 where a x1 x2 x3 b and in each case y1 y2 y3 y4 e R. Questions involving uniqueness implies uniqueness for solutions of boundary value
