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 of Solutions for a Class of Weighted p t -Laplacian System Multipoint Boundary Value Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 791762 18 pages doi 2008 791762 Research Article Existence of Solutions for a Class of Weighted p t -Laplacian System Multipoint Boundary Value Problems Qihu Zhang 1 2 3 Zheimei Qiu 2 and Xiaopin Liu2 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 College of Mathematics and Information Science Shaanxi Normal University Xi an Shaanxi 710062 China Correspondence should be addressed to Zheimei Qiu zhimeiqiu@ Received 12 June 2008 Accepted 22 October 2008 Recommended by Alberto Cabada This paper investigates the existence of solutions for weighted p t -Laplacian system multipoint boundary value problems. 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 2008 Qihu Zhang 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 of solutions for the following weighted p t -Laplacian system - p f w f u ỗf t u wft Styit V 0 t E 0 1 L1 with the following multipoint boundary value condition u 0 ZfiuW 30 u 1 52 tu ẻt 31 i 1 i 1 where p E C 0 1 R and p f 1 -ầp f w f u - w t u p -2u is called the weighted p t -Laplacian w E C 0 1 R satisfies 0 w f for all t E 0 1 and w t -1 p t -1 E L1 0 1 0 n pm-2 1 0 ẻ1 ịm-1 1 ai 0 pi 0 i 1 . m - 2 and 0 m-2ai 1 0 wpi 1 e0 e1 E RN Ô is a positive parameter. 2 Journal of Inequalities and Applications The study of differential equations and variational problems with variable exponent growth conditions is a new and interesting topic. Many .
