Open Access Research

A note on some nonlinear principal eigenvalue problems

Mohsen Boujary1* and Ghasem A Afrouzi2

Author Affiliations

1 Department of Mathematics, Science and Research Branch, Islamic, Azad University (Iau), Tehran, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

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Boundary Value Problems 2012, 2012:44 doi:10.1186/1687-2770-2012-44

Published: 16 April 2012

Abstract

We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) the boundary value problem

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/44/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/44/mathml/M1">View MathML</a>

where Ω ⊆ ℝN is a bounded domain, 1 < p < ∞ and α is a real number.

AMS Subject Classification: 35J60; 35B30; 35B40.

Keywords:
p-Laplacian; principal eigenvalue