A Neumann eigenvalue problem for fully nonlinear operators

Pages: 845 - 863, Volume 28, Issue 2, October 2010

doi:10.3934/dcds.2010.28.845       Abstract        Full Text (252.0K)       Related Articles

Isabeau Birindelli - Dipartimento di matematica "G. Castelnuovo”, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma, Italy (email)
Stefania Patrizi - Dipartimento di matematica "G. Castelnuovo”, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 Roma, Italy (email)

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 $+\infty$.

Keywords:  Eigenvalues, fully-nonlinear, Robin boundary condition.
Mathematics Subject Classification:  Primary: 35D40, 35J25; Secondary: 35P30.

Received: March 2010;      Revised: April 2010;      Published: April 2010.