A Neumann eigenvalue problem for fully nonlinear operators

Isabeau Birindelli; Stefania Patrizi

doi:10.3934/dcds.2010.28.845

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2010, Volume 28, Issue 2: 845-863. Doi: 10.3934/dcds.2010.28.845 open access

This issue Previous Article On some Schrödinger equations with non regular potential at infinity Next Article

A Neumann eigenvalue problem for fully nonlinear operators

Isabeau Birindelli^1, and
Stefania Patrizi^1,

1.
Dipartimento di matematica "G. Castelnuovo”, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma

Received: February 28, 2010

Revised: March 31, 2010

Published: June 2010

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Abstract

We prove the existence of the principal eigenvalues for the Pucci operators in bounded domains with boundary condition $\frac{\partial u}{\partial\vec n}=\alpha u$ corresponding respectively to positive and negative eigenfunctions and study their asymptotic behavior when $\alpha$ goes to $+\infty$.

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Mathematics Subject Classification: Primary: 35D40, 35J25; Secondary: 35P30.

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