tailieunhanh - Báo cáo hóa học: "Research Article Positive Solutions for Multiparameter Semipositone Discrete Boundary Value Problems via Variational Method"

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 Positive Solutions for Multiparameter Semipositone Discrete Boundary Value Problems via Variational Method | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 840458 15 pages doi 2008 840458 Research Article Positive Solutions for Multiparameter Semipositone Discrete Boundary Value Problems via Variational Method Jianshe Yu 1 2 Benshi Zhu 1 and Zhiming Guo2 1 College of Mathematics and Econometrics Hunan University Changsha 410082 China 2 College of Mathematics and Information Sciences Guangzhou University Guangzhou 510006 China Correspondence should be addressed to Jianshe Yu jsyu@ Received 13 March 2008 Accepted 24 August 2008 Recommended by Kanishka Perera We study the existence multiplicity and nonexistence of positive solutions for multiparameter semipositone discrete boundary value problems by using nonsmooth critical point theory and subsuper solutions method. Copyright 2008 Jianshe Yu 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. 1. Introduction Let Z and R be the set of all integers and real numbers respectively. For a b e Z define Z a a a 1 . Z a b a a 1 . b when a b. In this paper we consider the multiparameter semipositone discrete boundary value problem -A2u t - 1 Xf u ty fg u ty t e Z 1 N u 0 0 u N 1 0 where X f 0 are parameters N 4 is a positive integer Au t u t 1 -u t is the forward difference operator A2u t A Au t f 0 x R is a continuous positive function satisfying f 0 0 and g 0 x R is continuous and eventually strictly positive with g 0 0. We notice that for fixed f 0 Xf 0 fg 0 0 whenever X 0 is sufficiently small. We call a semipositone problem. Semipositone problems are derived from 1 where Castro and Shivaji initially called them nonpositone problems in contrast 2 Advances in Difference Equations with the terminology positone problems put forward by Keller and Cohen in 2 where the nonlinearity was positive and .