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Radially symmetric convex solutions for Dirichlet problems of Monge‐Ampère equations
Author(s) -
Liang Zaitao,
Chu Jifeng
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3789
Subject(s) - mathematics , dirichlet problem , regular polygon , monge–ampère equation , eigenvalues and eigenvectors , dirichlet distribution , mathematical analysis , fixed point theorem , pure mathematics , geometry , boundary value problem , physics , quantum mechanics
In this paper, we study the existence of radially symmetric convex solutions for Dirichlet problems of Monge‐Ampère equations. By applying a well‐known fixed point theorem in cones, we shall establish several new criteria for the existence of nontrivial radially symmetric convex solutions for the systems of Monge‐Ampère equations with or without an eigenvalue parameter. Copyright © 2015 John Wiley & Sons, Ltd.