(p, q) systems with critical terms in RN. (December 2018) - Fiscella, Alessio; Pucci, Patrizia
Abstract: This paper deals with the existence of nontrivial solutions for critical Hardy quasilinear systems ( S ) driven by general ( p, q ) elliptic operators of Marcellini types. Existence is derived as an application of the concentration-compactness principle of Lions via the mountain pass geometry. The constructed solution has both components nontrivial, that is it solves the actual system, which does not reduce into an equation. We present also a simplified version ( S ′ ) of the main system ( S ), which is anyway interesting. We exhibit a new proof for the existence of nontrivial solutions of ( S ), which is more direct and elegant. However, the assumptions for both systems ( S ) and ( S ′ ) are milder and in any case much different from the usual requests granted in related problems. Finally, the results improve or complement previous theorems for the quasilinear ( p, q ) scalar as well as vectorial problems.