Convex solutions of boundary value problem arising from Monge-Ampère equations

Shouchuan Hu; Haiyan Wang

doi:10.3934/dcds.2006.16.705

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2006, Volume 16, Issue 3: 705-720. Doi: 10.3934/dcds.2006.16.705

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Convex solutions of boundary value problem arising from Monge-Ampère equations

Shouchuan Hu^1, and
Haiyan Wang^2,

1.
College of Mathematics, Shandong Normal University, Jinan, Shandong
2.
Department of Mathematical Sciences & Applied Computing, Arizona State University, Phoenix, AZ 85069-7100

Received: September 30, 2005

Revised: April 30, 2006

Published: August 2006

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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.

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Mathematics Subject Classification: 34B15.

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