Heriot-Watt Mathematics Report Series
HWM97-23, 14 July 1997

On principal eigenvalues for boundary value problems with indefinite weight and Robin boundary conditions.

G A Afrouzi and K J Brown


Abstract

We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem $- \Delta u(x) = \lambda g(x)u(x)$ on $D$; $\frac{ \partial u}{\partial n}(x) + \alpha u(x) = 0$ on $\partial D$ where $D$ is a bounded region in $R^N$, $g$ is an indefinite weight function and $\alpha \in R$ may be positive, negative or zero. It is shown that two positive principal eigenvalues may exist when $\alpha < 0$.

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Full text: http://www.ma.hw.ac.uk/~ken/psfiles/ab_pams_97.ps.Z


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