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Research Article Existence and Asymptotic Behavior of Solutions for Weighted p t -Laplacian System Multipoint Boundary Value Problems in Half Line | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 926518 22 pages doi 10.1155 2009 926518 Research Article Existence and Asymptotic Behavior of Solutions for Weighted p t -Laplacian System Multipoint Boundary Value Problems in Half Line Zhimei Qiu 1 Qihu Zhang 1 2 and Yan Wang1 1 School of Mathematical Science Xuzhou Normal University Xuzhou Jiangsu 221116 China 2 Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou Henan 450002 China Correspondence should be addressed to Qihu Zhang zhangqh1999@yahoo.com.cn Received 5 January 2009 Accepted 20 June 2009 Recommended by Alberto Cabada This paper investigates the existence and asymptotic behavior of solutions for weighted p t -Laplacian system multipoint boundary value problems in half line. When the nonlinearity term f t satisfies sub- p- - 1 growth condition or general growth condition we give the existence of solutions via Leray-Schauder degree. Copyright 2009 Zhimei Qiu 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 In this paper we consider the existence and asymptotic behavior of solutions for the following weighted p t -Laplacian system -ầ.p tyu ỗf t u w 1 u 0 t E 0 x 1.1 u 0 lim uft lim w f u pt 2u t lim w t u p t 2u t 1.2 t t 0 t where p E C 0 o R p t 1 limt x p f exists and limt x p f 1 -bp tyu - w t u p -2u is called the weighted p f -Laplacian w E C 0 to R satisfies 0 w t for all t E 0 to and w f -1 p -1 E L1 0 x the equivalent liTti P r 2 1 lỉm 7I1Í t W i p p r 11 í ỉ m pcifiQ til of lìm nj-Titi rillp p r 21 nnir 0 Cwyr u u yr J lilllr_ TO iwyr J u u yr J means that llillr_ 0 Cwyr u u yr J and limr w r u p r -2u r both exist and equal Ỗ is a positive parameter. 2 Journal of Inequalities and Applications The study of differential .