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Open Access Research

Half-linear eigenvalue problem: Limit behavior of the first eigenvalue for shrinking interval

Gabriella Bognár1 and Ondřej Došlý2*

Author Affiliations

1 University of Miskolc, Egyetemváros, Miskolc, 3515, Hungary

2 Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, Brno, 611 37, Czech Republic

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Boundary Value Problems 2013, 2013:221  doi:10.1186/1687-2770-2013-221

Published: 7 November 2013

Abstract

We investigate the limit behavior of the first eigenvalue of the half-linear eigenvalue problem when the length of the interval tends to zero. We show that the important role is played by the limit behavior of ratios of primitive functions of coefficients in the investigated half-linear equation.

MSC: 34C10.