A Courant nodal domain theorem for linearized mean field type equations
Daniele Bartolucci, Aleks Jevnikar, Ruijun Wu
TL;DR
This paper investigates the nodal domain properties of eigenfunctions of a linearized nonlocal operator derived from a mean field type equation, providing estimates and uniqueness results.
Contribution
It introduces a Courant nodal domain theorem adapted to the linearized nonlocal operator of a mean field equation, offering new insights into eigenfunction properties.
Findings
Estimated the number of nodal domains for radial eigenfunctions
Established uniqueness properties related to the eigenfunctions
Extended Courant's theorem to a nonlocal operator context
Abstract
We are concerned with the analysis of a mean field type equation and its linearization, which is a nonlocal operator, for which we estimate the number of nodal domains for the radial eigenfunctions and the related uniqueness properties.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Differential Equations and Boundary Problems · Numerical methods in inverse problems