Abstract In this paper, we focus on the existence of positive solutions to following planar Schrödinger–Newton system with general critical exponential growth $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta {u}+u+\phi u =f(u)&amp;{} \text{ in }\,\,\mathbb {R}^2, \\ \Delta {\phi }=u^2 &amp;{} }\,\, \mathbb \end{array} \right. \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/M...

Abstract In this paper, we complete the study started in Ambrosio and Rădulescu (J Math Pures Appl (9) 142:101–145, 2020) on concentration phenomena for a class of fractional ( p , q )-Schrödinger equations involving critical Sobolev exponent. More precisely, focus our attention following )-Laplacian problems: $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}_{p}u+(-\Delta )^{s}_{q}u +...