A Sturm Liouville theorem for quadratic operator pencils

2019/07/12 by Sukhtayev, Alim, Zumbrun, Kevin
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.05679

Abstract

We establish a SturmLiouville theorem for quadratic operator pencils counting their unstable real roots, with applications to stability of waves. Such pencils arise, for example, in reduction of eigenvalue systems to higher-order scalar problems.

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