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

G. A. Afrouzi

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 30, 1-5

Abstract:

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

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:697818

DOI: 10.1155/S0161171202007780

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