Nontrivial $ p $-convex solutions to singular $ p $-Monge-Ampère problems: Existence, Multiplicity and Nonexistence

Abstract

<abstract><p>Our main objective of this paper is to study the singular $ p $-Monge-Ampère problems: equations and systems of equations. New multiplicity results of nontrivial $ p $-convex radial solutions to a single equation involving $ p $-Monge-Ampère operator are first analyzed. Then, some new criteria of existence, nonexistence and multiplicity for nontrivial $ p $-convex radial solutions for a singular system of $ p $-Monge-Ampère equation are also established.</p></abstract>