Convex solutions of boundary value problems arising from monge-ampère equations

Shouchuan Hu; Haiyan Wang

Convex solutions of boundary value problems arising from monge-ampère equations

Shouchuan Hu, Haiyan Wang

Mathematical and Natural Sciences, School of (SMNS)

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

Original language	English (US)
Pages (from-to)	705-720
Number of pages	16
Journal	Discrete and Continuous Dynamical Systems
Volume	16
Issue number	3
State	Published - Nov 1 2006

Keywords

Boundary value problem
Fixed index theorem
Monge-Ampère equation
Strictly convex solution

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "Convex solutions of boundary value problems arising from monge-amp{\`e}re equations",

abstract = "In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Amp{\`e}re equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.",

keywords = "Boundary value problem, Fixed index theorem, Monge-Amp{\`e}re equation, Strictly convex solution",

author = "Shouchuan Hu and Haiyan Wang",

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language = "English (US)",

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AU - Wang, Haiyan

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N2 - In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

AB - In this paper we study an eigenvalue boundary value problem which arises when seeking radial convex solutions of the Monge-Ampère equations. We shall establish several criteria for the existence, multiplicity and nonexistence of strictly convex solutions for the boundary value problem with or without an eigenvalue parameter.

KW - Boundary value problem

KW - Fixed index theorem

KW - Monge-Ampère equation

KW - Strictly convex solution

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Convex solutions of boundary value problems arising from monge-ampère equations

Abstract

Keywords

ASJC Scopus subject areas

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