Nonlocal elliptic systems of N-Kirchhoff type with exponential growth - Tordecilla, Jesus Alberto Leon (Topological Methods in Nonlinear Analysis, 2025)
In this work, we are devoted to establishing the existence of positive solutions for a nonlocal elliptic system of N-Kirchhoff type on bounded domains in R^N with N≥ 2. The nonlinearity considered in the equation combined a nonlocal term with an exponential term governed by the Trudinger-Moser inequality, which may be subcritical, critical or supercritical. We use the Galerkin approximation together with a variant of the Brouwer Fixed Point Theorem in the product of Sobolev spaces.