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Báo cáo hóa học: " Research Article Existence and Asymptotic Behavior of Solutions for Weighted p t -Laplacian Integrodifferential System Multipoint and Integral Boundary Value Problems in Half Line"

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 Asymptotic Behavior of Solutions for Weighted p t -Laplacian Integrodifferential System Multipoint and Integral Boundary Value Problems in Half Line | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 965313 26 pages doi 10.1155 2010 965313 Research Article Existence and Asymptotic Behavior of Solutions for Weighted p t -Laplacian Integrodifferential System Multipoint and Integral Boundary Value Problems in Half Line Yan Wang 1 2 Yunrui Guo 3 and Qihu Zhang1 2 1 Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou Henan 450002 China 2 School of Mathematical Science Xuzhou Normal University Xuzhou Jiangsu 221116 China 3 Department of Mathematics Henan Institute of Science and Technology Xinxiang Henan 453003 China Correspondence should be addressed to Qihu Zhang zhangqh1999@yahoo.com.cn Received 5 February 2010 Revised 13 June 2010 Accepted 28 June 2010 Academic Editor P. J. Y. Wong Copyright 2010 Yan Wang 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. This paper investigates the existence and asymptotic behavior of solutions for weighted p t -Laplacian integro-differential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies sub- p- - 1 growth condition or general growth condition we give the existence of solutions via Leray-Schauder degree. Moreover the existence of nonnegative solutions has been discussed. 1. Introduction In this paper we consider the existence and asymptotic behavior of solutions for the following weighted p t -Laplacian integrodifferential system -àpụyu ỗf t u wityA r ul S u T u 0 t e 0 x 1.1 with the following multipoint and integral boundary value condition m-2 u 0 ỵ ữiu ịi gQ i 1 to lim u L e ifu ifdt t to 0 1.2 2 Journal of Inequalities and Applications where u 0 x RN S and T are linear operators defined by S u d y s t u s ds 0 T u f f x s t u s ds 0 1.3 where y e C D R X