Maximum principles, ABP estimates and HKS inequalities related to GLE systems

Closely related to the pioneering work (Berestycki et al. Commun Pure Appl Math, pp 47–92, 1994) by the authors Berestycki, Nirenberg and Varadhan, we prove maximum and comparison principles for generalized Lane-Emden type systems and as consequences we establish Aleksandrov-Bakelman-Pucci estimates and Harnack-Krylov-Safonov inequalities for related non-homogeneous inequalities, among other results. These contributions go towards a comprehensive understanding on strongly coupled nonlinear elliptic systems.