A necessary and sufficient condition for the existence of large solutions to ‘mixed’ type elliptic systems - Zhang, Xinguang (Elsevier, 2012)
In this paper, we substantially solve an open problem proposed by Alan Lair for the system of the form ?u=p(|x|)va?u=p(|x|)va and ?v=q(|x|)uß,(x?Rn(n?3))?v=q(|x|)uß,(x?Rn(n?3)) in the sense that, we find more general conditions on f,gf,g in order to obtain an analog existence result as for the particular case f(s)=saf(s)=sa and g(s)=sßg(s)=sß 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].