Asymptotic and optimal Liouville properties for Wolff type integral systems

Authors

John Villavert, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

1-2016

Abstract

This article examines the properties of positive solutions to fully nonlinear systems of integral equations involving Hardy and Wolff potentials. The first part of the paper establishes an optimal existence result and a Liouville type theorem for the integral systems. Then, the second part examines the decay rates of positive bound states at infinity. In particular, a complete characterization of the asymptotic properties of bounded and decaying solutions is given by showing that such solutions vanish at infinity with two principle rates: the slow decay rates and the fast decay rates. In fact, the two rates can be fully distinguished by an integrability criterion. As an application, the results are shown to carry over to certain systems of quasilinear equations.

Comments

© 2015 Elsevier Ltd. All rights reserved. Original published version available at https://doi.org/10.1016/j.na.2015.09.017

Recommended Citation

Villavert, John. 2016. “Asymptotic and Optimal Liouville Properties for Wolff Type Integral Systems.” Nonlinear Analysis 130 (January): 102–20. https://doi.org/10.1016/j.na.2015.09.017.

First Page

102

Last Page

120

Publication Title

Nonlinear Analysis

DOI

10.3934/dcds.2016094