tailieunhanh - Báo cáo hóa học: " Research Article Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations"

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 Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations | Hindawi Publishing Corporation Boundary Value Problems Volume 2007 Article ID 16407 8 pages doi 2007 16407 Research Article Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations Zuodong Yang and Bing Xu Received 29 June 2006 Accepted 17 October 2006 Recommended by Shujie Li We consider the problem -div Vu p-2Vu a x um Aun x e RN N 3 where 0 m p - 1 n a x 0 a x is not identically zero. Under the condition that a x satisfies H we show that there exists A0 0 such that the above-mentioned equation admits at least one solution for all A e 0 Ao . This extends the results of Laplace equation to the case of p-Laplace equation. Copyright 2007 Z. Yang and B. Xu. 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. In this work we are interested in studying the existence of solutions to the following quasilinear equation -div Vu p-2Vu a x um Aun x e RN N 3 1 where 0 m p - 1 n a x 0 a x is not identically zero. We will assume throughout the paper that a x e C RN . Equations of the above form are mathematical models occuring in studies of the p-Laplace equation generalized reaction-diffusion theory 1 non-Newtonian fluid theory and the turbulent flow of a gas in porous medium 2 . In the non-Newtonian fluid theory the quantity p is characteristic of the medium. Media with p 2 are called dilatant fluids and those with p 2 are called pseudoplastics. If p 2 they are Newtonian fluids. Problem 1 for bounded domains with zero Dirichlet condition has been extensively studied even for more general sublinear functions . We refer in particular to 3-10 see also the references therein . When p 2 the related results have been obtained by 1116 including bounded domains with zero Dirichlet condition or RN . Our existence 2 Boundary Value Problems results extend that of Brezis and Kamin see 11 Theorem 1 for .