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

In this paper, we substantially solve an open problem proposed by Alan Lair for the system of the form Δ u = p ( | x | ) v α and Δ v = q ( | x | ) u β , ( x ∈ 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 α and g ( s ) = s β 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].