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 fora nonlocal elliptic system of $N$-Kirchhoff type on bounded domains in $\mathbb{R}^N$ 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.