Computational Methods and Function Theory 6 (2006), No. 1, 29--36
Copyright Heldermann Verlag 2006
Robert Trickey
pmxrvt@nottingham.ac.uk , School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, U.K.
A variety of scenarios in electrostatics can be modeled using functions of the form $f(z) = \sum_{k=1}^{\infty}a_k/(z-z_k)$. In these models, zeros of the function correspond to equilibrium points in the electrostatic field. We strengthen some previous existence results for zeros of functions of the form $f$. Also, similar techniques are applied for proving the existence of critical points of potentials in $n$-dimensional real space, $n \geq 3$.
Keywords: Critical points, logarithmic potentials, zeros of meromorphic functions.
MSC 2000: 31A05, 30D30, 31B05.
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