Advances in Differential Equations

Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators

Françoise Demengel

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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.

Article information

Source
Adv. Differential Equations Volume 14, Number 11/12 (2009), 1107-1126.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854786

Mathematical Reviews number (MathSciNet)
MR2560870

Zentralblatt MATH identifier
1196.35088

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations 35J60: Nonlinear elliptic equations 35P15: Estimation of eigenvalues, upper and lower bounds 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory

Citation

Demengel, Françoise. Nonuniqueness of solutions for Dirichlet problems related to fully nonlinear singular or degenerate operators. Adv. Differential Equations 14 (2009), no. 11/12, 1107--1126. https://projecteuclid.org/euclid.ade/1355854786.


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