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 Bessel’s Differential Equation and Its Hyers-Ulam Stability | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 21640 8 pages doi 2007 21640 Research Article Bessel s Differential Equation and Its Hyers-Ulam Stability Byungbae Kim and Soon-Mo Jung Received 23 August 2007 Accepted 25 October 2007 Recommended by Panayiotis D. Siafarikas We solve the inhomogeneous Bessel differential equation and apply this result to obtain a partial solution to the Hyers-Ulam stability problem for the Bessel differential equation. Copyright 2007 B. Kim and . Jung. 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 In 1940 Ulam gave a wide ranging talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of important unsolved problems see 1 . Among those was the question concerning the stability of homomorphisms let G1 be a group and let G2 be a metric group with a metric d . Given any 8 0 does there exist an e 0 such that if a function h G1 G2 satisfies the inequality d h xy h x h y e for all x y e G1 then there exists a homomorphism H G1 G2 with d h x H x 8 for all x e G1 In the following year Hyers 2 partially solved the Ulam problem for the case where G1 and G2 are Banach spaces. Furthermore the result of Hyers has been generalized by Rassias see 3 . Since then the stability problems of various functional equations have been investigated by many authors see 4-6 . We will now consider the Hyers-Ulam stability problem for the differential equations assume that X is a normed space over a scalar field K and that I is an open interval where K denotes either R or C. Let a0 a1 . an I K be given continuous functions let g I X be a given continuous function and let y I X be an n times continuously differentiable function satisfying the inequality I an t y n t an-1 t y n 1 t a1 t y t a0
