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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