Sign-changing solutions for a critical exponential problem with competing potentials - Barahona, Willy; Lapa, Eugenio Cabanillas; Figueiredo, Giovany M. (Topological Methods in Nonlinear Analysis, 2025)
We establish the existence, concentration, and exponential decay of a family of sign-changing solutions for a problem involving exponential critical growth, described by the equation: cases -ε^2div(a(x) abla u)+V(x)u =K(x) f(u) & in R^2, u H^1(R^2). cases (P_ε) To address the lack of compactness and the competition between the potentials, we employ variational methods alongside a suitable truncation of the nonlinearity.