Negative Power Nonlinear Integral Equations on Bounded Domains

Abstract

This is the continuation of our previous work [5], where we introduced and studied some nonlinear integral equations on bounded domains that are related to the sharp Hardy-Littlewood-Sobolev inequality. In this paper, we introduce some nonlinear integral equations on bounded domains that are related to the sharp reversed Hardy-Littlewood-Sobolev inequality. These are integral equations with nonlinear term involving negative exponents. Existence results as well as nonexistence results are obtained.

arXiv comment20 pages

References in corpus (1)

• Semilinear equations involving the fractional Laplacian on domains

Cited by in corpus (1)

• Extremal problem of Hardy-Littlewood-Sobolev inequalities on compact Riemannian manifolds