TAILIEUCHUNG - Báo cáo hóa học: " Research Article Existence Result for a Class of Elliptic Systems with Indefinite Weights in R2"

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 Result for a Class of Elliptic Systems with Indefinite Weights in R2 | Hindawi Publishing Corporation Boundary Value Problems Volume 2008 Article ID 217636 10 pages doi 2008 217636 Research Article Existence Result for a Class of Elliptic Systems with Indefinite Weights in R2 Guoqing Zhang1 and Sanyang Liu2 1 College of Sciences University of Shanghai for Science and Technology Shanghai 200093 China 2 Department of Applied Mathematics Xidian University Xi an 710071 China Correspondence should be addressed to Guoqing Zhang zgqw2001@ Received 31 October 2007 Accepted 4 March 2008 Recommended by Zhitao Zhang We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in R2. The proofs base on Trudinger-Moser inequality and a generalized linking theorem introduced by Kryszewski and Szulkin. Copyright 2008 G. Zhang and S. Liu. 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 In this paper we study the existence of a nontrivial solution for the following systems of two semilinear coupled Poisson equations P -Au u g x v -Av v f x u x R2 x R2 where f x f and g x f are continuous functions on R2 X R and have the maximal growth on t which allows to treat problem P variationally A is the Laplace operator. Recently there exists an extensive bibliography in the study of elliptic problem in RN 1-6 . As dimensions N 3 in 1998 de Figueiredo and Yang 5 considered the following coupled elliptic systems -Au u g x v x RN -Av v f x u x RN 2 Boundary Value Problems where f g are radially symmetric in x and satisfied the following Ambrosetti-Rabinowitz condition f x s ds c t 2 61 0 t g x s ds c t 0 2 62 vt R and for some 61 0 62 0. They obtained the decay symmetry and existence of solutions for problem . In 2004 Li and Yang 6 proved that problem possesses at least a positive solution when

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