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Spectral loci of Sturm-Liouville operators with polynomial potentials
[unknown]
2014
Spectral Theory and Differential Equations
unpublished
Preserved Fulltext
We consider differential equations −y ′′ + P (z, a)y = λy, where P is a polynomial of the independent variable z depending on a parameter a. The spectral locus is the set of (a, λ) such that the equation has a non-trivial solution tending to zero on two fixed rays in the complex plane. We study the topology of the spectral loci for polynomials P of degree 3 or 4 with respect to z. MSC: 81Q05, 34M60, 34A05. Theorem 7 [11] The points (b, λ) ∈ Z QES J where the level crossing occurs are the
doi:10.1090/trans2/233/08
fatcat:sg2itpvihjhh7efyherd7ji6zu