Đang chuẩn bị liên kết để tải về tài liệu:
Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 496417,

Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011, Article ID 496417, 16 pages doi:10.1155/2011/496417 Research Article Existence of Solutions for a Nonlinear Elliptic Equation with General Flux Term Hee Chul Pak Department of Applied Mathematics, Dankook University, Cheonan, Chungnam 330-714, Republic of Korea Correspondence should be addressed to Hee Chul Pak, hpak@dankook.ac.kr Received 25 September 2010; Revised 29 January 2011; Accepted 27 February 2011 Academic Editor: D. R. Sahu Copyright q 2011 Hee Chul Pak. 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. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 496417 16 pages doi 10.1155 2011 496417 Research Article Existence of Solutions for a Nonlinear Elliptic Equation with General Flux Term Hee Chul Pak Department of Applied Mathematics Dankook University Cheonan Chungnam 330-714 Republic of Korea Correspondence should be addressed to Hee Chul Pak hpak@dankook.ac.kr Received 25 September 2010 Revised 29 January 2011 Accepted 27 February 2011 Academic Editor D. R. Sahu Copyright 2011 HeeChulPak. 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 prove the existence of solutions for an elliptic partial differential equation having more general flux term than either p-Laplacian or flux term of the Leray-Lions type conditions - Zflfld dxj a uXj. uX f. Brouwer s fixed point theorem is one of the fundamental tools of the proof. 1. Introduction We are concerned with problems of partial differential equations such as a nonlinear elliptic equation -V- J f 1.1 which contains the flux term J. The flux term J is a vector field that explains a movement of some physical contents u such as temperature chemical potential electrostatic potential or fluid flows. Physical observations tell us in general that J depends on u and approximately on its gradient at each point x that is J J x V u x . For linear cases one can simply represent J as J cVu on isotropic medium or J AVu with a square matrix A on an isotropic medium . But for nonlinear cases the situation can be much more complicated. One of the common assumptions is that J Vu p-2 Vu is to produce the p-Laplacian Apu V- Vu p-2Vu. 1.2 2 Fixed Point Theory and Applications Slightly more general conditions for example the Leray-Lions type conditions might be placed on J but it is too good to be true that the flux term has those kinds of