Solutions of Liouville equations with non-trivial profile in dimensions 2 and 4
Roberto Albesiano
Abstract:We prove the existence of a family of non-trivial solutions of the Liouville equation in dimensions two and four with infinite volume. These solutions are perturbations of a finite-volume solution of the same equation in one dimension less. In particular, they are periodic in one variable and decay linearly to −∞ in the other variables. In dimension two, we also prove that the periods are arbitrarily close to πk, k ∈ N (from the positive side). The main tool we employ is bifurcation theory in weighted Hölder s… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.