Hindawi Publishing Corporation Boundary Value Problems Volume 2010, Article ID 607453, 17 pages doi: Research Article Existence and Nonexistence of Positive Solutions for Singular p-Laplacian Equation in Ê N Caisheng Chen, Zhenqi Wang, and Fengping Wang Department of Mathematics, Hohai University, Nanjing, Jiangsu 210098, China Correspondence should be addressed to Caisheng Chen, cshengchen@ Received 15 August 2010; Accepted 10 December 2010 Academic Editor: Zhitao Zhang Copyright q 2010 Caisheng Chen 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. We. | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 607453 17 pages doi 2010 607453 Research Article Existence and Nonexistence of Positive Solutions for Singular p-Laplacian Equation in RN Caisheng Chen Zhenqi Wang and Fengping Wang Department of Mathematics Hohai University Nanjing Jiangsu 210098 China Correspondence should be addressed to Caisheng Chen cshengchen@ Received 15 August 2010 Accepted 10 December 2010 Academic Editor Zhitao Zhang Copyright 2010 Caisheng Chen 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. We study the existence and nonexistence of solutions for the singular quasilinear problem -div x -ap Vu p-2Vu h x f u XH x g u x M u x 0 x M lim x TOw x 0 where 1 p N 0 a N - p p and f u and g u behave like um and un with 0 m p - 1 n at the origin. We obtain the existence by the upper and lower solution method and the nonexistence by the test function method. 1. Introduction In this paper we study through the upper and lower solution method and the test function method the existence and nonexistence of solution to the singular quasilinear elliptic problem - divộx ap Vu p 2 Vu h x f u AH xjg Ù x e RN u x 0 x Ck lim u x 0 x TO with 1 p N 0 a N - p p A 0. h x H x RN 0 to are the locally Holder continuous functions not identically zero and f u and g u are locally Lipschitz continuous functions. The study of this type of equation in is motivated by its various applications for instance in fluid mechanics in Newtonian fluids in flow through porous media and in glaciology see 1 . The equation in involves singularities not only in the nonlinearities but also in the differential operator. 2 Boundary Value Problems Many authors studied this kind of problem for the case a 0 see 2-7 In these works the nonlinearities have sublinear and .
