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September  2006, 16(3): 705-720. doi: 10.3934/dcds.2006.16.705

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, China
2. 

Department of Mathematical Sciences & Applied Computing, Arizona State University, Phoenix, AZ 85069-7100, United States

Received  October 2005 Revised  May 2006 Published  August 2006

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.
Keywords: strictly convex solution, fixed index theorem., boundary value problem, Monge-Ampère equation.
Mathematics Subject Classification: 34B1.
Citation: Shouchuan Hu, Haiyan Wang. Convex solutions of boundary value problem arising from Monge-Ampère equations. Discrete & Continuous Dynamical Systems, 2006, 16 (3) : 705-720. doi: 10.3934/dcds.2006.16.705
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