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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 Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 586020 16 pages doi 10.1155 2008 586020 Research Article Existence and Multiple Solutions for Nonlinear Second-Order Discrete Problems with Minimum and Maximum Ruyun Ma and Chenghua Gao College of Mathematics and Information Science Northwest Normal University Lanzhou 730070 China Correspondence should be addressed to Ruyun Ma mary@nwnu.edu.cn Received 15 March 2008 Revised 6 June 2008 Accepted 19 July 2008 Recommended by Svatoslav Stanek Consider the multiplicity of solutions to the nonlinear second-order discrete problems with minimum and maximum A 2u k-1 f k u k Au k k e T min u k k e T A max u k k e T B where f T X R 2 R a b e N are fixed numbers satisfying b a 2 and A B e R are satisfying B A T a 1 . . b - 1 T a a 1 . . b - 1 b . Copyright 2008 R. Ma and C. Gao. 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 Let a b e N a 2 b T a 1 . . b - 1 T a a 1 . b - 1 b . Let E u u T - R 1.1 and for u e E let u s max u k . 1.2 keT Let E u u T - R 1.3 and for u e E let u e max u k . 1.4 keT It is clear that the above are norms on E and E respectively and that the finite dimensionality of these spaces makes them Banach spaces. 2 Advances in Difference Equations In this paper we discuss the nonlinear second-order discrete problems with minimum and maximum A2u k - 1 f k u k àu k k e T 1.5 min u k k e T A max u k k e T B 1.6 where f T X R2 R is a continuous function a b e N are fixed numbers satisfying b a 2 and A B e R satisfying B A. Functional boundary value problem has been studied by several authors 1-7 . But most of the papers studied the differential equations functional boundary value problem 1-6 . As we know the study of difference equations represents a very important field in mathematical research 8-12
