International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 34301, 17 pages
Global Existence and Blow-Up Solutions and Blow-Up Estimates for Some Evolution Systems with
-Laplacian with Nonlocal Sources
1Institute of Mathematics, School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China
2College of Zhongbei, Nanjing Normal University, Nanjing 210046, China
Received 20 September 2006; Accepted 21 February 2007
Academic Editor: Alfonso Castro
Copyright © 2007 Zhoujin Cui and Zuodong Yang. 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.
This paper deals with -Laplacian systems , , , , with null Dirichlet boundary conditions in a smooth bounded domain
, where , . We first get the nonexistence result for related elliptic systems of nonincreasing positive solutions. Secondly by using this nonexistence result, blow up estimates for above -Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under . Then under appropriate hypotheses, we establish local theory of the
solutions and obtain that the solutions either exist globally or blow up in finite time.