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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 1, Pages 25-29
http://dx.doi.org/10.1155/S0161171202007780

Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions

Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran

Received 24 June 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: Δu(x)=λg(x)u(x), xD;(u/n)(x)+αu(x)=0, xD, where Δ is the standard Laplace operator, D is a bounded domain with smooth boundary, g:D is a smooth function which changes sign on D and α. We discuss the relation between α and the principal eigenvalues.