tailieunhanh - Báo cáo hóa học: " Research Article The Method of Subsuper Solutions for Weighted p r -Laplacian Equation Boundary Value Problems"

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 The Method of Subsuper Solutions for Weighted p r -Laplacian Equation Boundary Value Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 621621 19 pages doi 2008 621621 Research Article The Method of Subsuper Solutions for Weighted p r -Laplacian Equation Boundary Value Problems Qihu Zhang 1 2 Xiaopin Liu 2 and Zhimei Qiu2 1 Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou Henan 450002 China 2 School of Mathematics Science Xuzhou Normal University Xuzhou Jiangsu 221116 China Correspondence should be addressed to Zhimei Qiu zhimeiqiu@ Received 23 May 2008 Accepted 21 August 2008 Recommended by Marta Garcia-Huidobro This paper investigates the existence of solutions for weighted p r -Laplacian ordinary boundary value problems. Our method is based on Leray-Schauder degree. As an application we give the existence of weak solutions for p x -Laplacian partial differential equations. 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 pfr -Laplacian ordinary equation with right-hand terms depending on the first-order derivative í I p r 2 V l p r -l PI Vrcl 1 - wự u I u f r u w rl u - vr e Ự1 ty d with one of the following boundary value conditions u T1 c u T2 d 1 .p T 1 g u T1 w T1 u T1Ỵ 0 u T2 d 1 p T1 11 p T2 1 g u T1 WTw u T1 0 h u T2 w T2 u T2 0 p T 2 pCTz 2 u T u T2 w T1 u T1 p u T1 WT2 u T2 p 2 u T2 where p e C T1 T2 R and p r 1 w e C T1 T2 R satisfies 0 w r Vr e T1 T2 and w r 1 ph 1 e L1 T1 T2 w r u p r 2u is called the weighted p r -Laplacian the 2 Journal of Inequalities and Applications notation w T1 1 p T1 1 u T1 means limr T w r 1 p r 1 u r exists and Z T 1 p T1 -1 1 p r -1 wiD 1 u TA lim w r u r z z y T z z similarly 1 p Tz -1 1 p r