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November/December 2009 Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators
Françoise Demengel
Adv. Differential Equations 14(11/12): 1107-1126 (November/December 2009).

Abstract

We study the Dirichlet problem for fully nonlinear elliptic operators: $G(D^2u, \nabla u, u, x) = f(x)$ in $\Omega$, where $\Omega$ is a bounded regular domain, and $f$ is continuous. We prove the existence, the nonexistence and the multiplicity of solutions for some particular right-hand side $f$ when $G$ has its two principal eigenvalues of different sign.

Citation

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Françoise Demengel. "Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators." Adv. Differential Equations 14 (11/12) 1107 - 1126, November/December 2009.

Information

Published: November/December 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1196.35088
MathSciNet: MR2560870

Subjects:
Primary: 35J25, 35J60, 35P15, 35P30

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 11/12 • November/December 2009
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