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

Abstract

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.

Keywords

• singular $ p $-monge-ampère equations and systems
• nontrivial $ p $-convex solutions
• fixed point index
• multiplicity