On a Elliptic System Involving Nonhomogeneous Nonlinearities and Critical Growth.

Let Ω ⊂ R N be a bounded domain with N ≥ 3 . We address the existence and nonexistence of solutions for the following class of elliptic systems: - Δ u = a u + b v + μ | u | p - 2 u in Ω - Δ v = b u + a v + | v | 2 ∗ - 2 v in Ω <graphic href="574_2023_337_Article_Equ22.gif"></graphic> with Dirichlet boundary condition, where a , b ∈ R , the exponent p > 1 , μ ∈ R is a parameter and 2 ∗ = 2 N / (N - 2) is the critical Sobolev exponent. By exploiting minimization arguments, minimax techniques and a Pohozaev identity, we obtain various results for the above system by analyzing the interplay between a , b , μ and the exponent p. [ABSTRACT FROM AUTHOR]