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 Positive Solutions to p(x)-Laplacian Equations with Singular Nonlinearities | Hindawi Publishing Corporation Journal ofInequalities and Applications Volume 2007 Article ID 19349 9 pages doi 2007 19349 Research Article Existence and Asymptotic Behavior of Positive Solutions to p x -Laplacian Equations with Singular Nonlinearities Qihu Zhang Received 17 July 2007 Accepted 27 August 2007 Recommended by M. Garcia-Huidobro This paper investigates the p x -Laplacian equations with singular nonlinearities - Ap x u Ằ uY x in o u x 0 on do where -Ap X U -div Vu p x -2Vu is called p x -Laplacian. The existence of positive solutions is given and the asymptotic behavior of solutions near boundary is discussed. Copyright 2007 Qihu Zhang. 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 The study of differential equations and variational problems with nonstandard p x -growth conditions is a new and interesting topic. We refer to 1 2 the background of these problems. Many results have been obtained on this kind of problems for example 2-13 . In 4 7 Fan and Zhao give the regularity of weak solutions for differential equations with nonstandard p x -growth conditions. On the existence of solutions for p x -Laplacian problems in bounded domain we refer to 5 11 12 . In this paper we consider the p x -Laplacian equations with singular nonlinearities A -Ap x u uYx in P u x 0 on do where -Ap x U - div Vu p x -2Vu is called p x -Laplacian o c RN is a bounded domain with C2 boundary do. If p x p a constant then P is the well-known p-Laplacian problem. There are many results on the existence of positive solutions for p-Laplacian problems with singular nonlinearities see 14-18 but the results on the existence of positive solutions for p x -Laplacian problems with singular nonlinearities 2 Journal of Inequalities and Applications are rare. Our aim is to give the existence of positive .
