Schrödinger-poisson system with zero mass in R2 involving (2, q)-Laplacian: existence, asymptotic behavior and regularity of solutions.

It is established the existence of positive least energy solution for the following class of planar elliptic systems in the zero mass case - Δ u - Δ q u + ϕ | u | r - 2 u = λ | u | p - 2 u , in R 2 , Δ ϕ = 2 π | u | r , & in R 2 , where λ ≥ 0 , 1 < q < 2 , q ∗ : = 2 q / (2 - q) < r < ∞ and p ≥ 2 r . Due to the nature of the problem, we deal with the logarithmic integral kernel. Our approach is based on Nehari manifold and a version of the Principle of Symmetric Criticality due to Palais. Furthermore, we study the asymptotic behavior of the solutions whenever the parameter λ goes to zero or infinity. Finally, we study regularity of solutions applying Moser iteration scheme. [ABSTRACT FROM AUTHOR]