We study the prototype model of the boundary value problem where () is a connected smooth domain, and the exponents and are non-negative numbers. Under appropriate conditions on the exponents , , , and , and on the domain , a variety of results on a priori estimates, existence and non-existence of positive solutions have been established.
Henghui ZOU. "Existence and non-existence for strongly coupled quasi-linear cooperative elliptic systems." J. Math. Soc. Japan 59 (2) 393 - 421, April, 2007. https://doi.org/10.2969/jmsj/05920393