A necessary and sufficient condition for the existence of large solutions to 'mixed' type elliptic systems

作者：Zhang, Xinguang^*

来源：Applied Mathematics Letters, 2012, 25(12): 2359-2364.

DOI：10.1016/j.aml.2012.07.002

• Necessary and sufficient condition
• Elliptic system
• Large solution
• Entire solution

In this paper, we substantially solve an open problem proposed by Alan Lair for the system of the form Delta u = p(vertical bar x vertical bar)upsilon(alpha) and Delta upsilon = q(vertical bar x vertical bar)u(beta), (x is an element of R-n (n >= 3)) in the sense that, we find more general conditions on f, g in order to obtain an analog existence result as for the particular case f (s) = s(alpha) and g (s) = s(beta) treated in [A. Lair, A necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems, J. Math. Anal. Appl. 365 (2010)103-108].

• 出版日期2012-12
• 单位烟台大学