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

Meiqiang Feng; Meiqiang Feng

doi:10.3934/cam.2024004

Communications in Analysis and Mechanics

2024, Volume 16, Issue 1: 71-93. doi: 10.3934/cam.2024004

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

Meiqiang Feng ^,

School of Applied Science, Beijing Information Science & Technology University, Beijing, 100192, PR China

Received: 05 September 2023 Revised: 18 December 2023 Accepted: 09 January 2024 Published: 17 January 2024
35J96, 35J57

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.
- singular $ p $-Monge-Ampère equations and systems,
- nontrivial $ p $-convex solutions,
- fixed point index,
- multiplicity
Citation: Meiqiang Feng. Nontrivial $ p $-convex solutions to singular $ p $-Monge-Ampère problems: Existence, Multiplicity and Nonexistence[J]. Communications in Analysis and Mechanics, 2024, 16(1): 71-93. doi: 10.3934/cam.2024004

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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.

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