The existence and nonexistence of entire positive solutions of semilinear elliptic systems with gradient term

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:371

Article

Zhang, Xinguang¹  Liu, Lishan² 

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China

[2] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

关键词: Large solution;    Semilinear elliptic problem;    Bounded solution;    Entire solution;   

DOI  :  10.1016/j.jmaa.2010.05.029

来源: Elsevier

【 摘 要 】

We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Delta u + vertical bar del v vertical bar = q(vertical bar x vertical bar)f(u, v) Delta v + vertical bar del v vertical bar = q(vertical bar x vertical bar)g(u, v) on R(N), N >= 3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free