Geodesic
Indefinite Sturm Theory
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 91-96.

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The symplectic versions of the Sturm oscillation and comparison theorem describe some properties of the Maslov index and were proved by developing a suitable intersection theory in the Lagrangian Grassmannian setting. What we propose here is a Sturm oscillation and comparison theorem for indefinite systems, obtained by defining a new index by means of the Brouwer degree of a determinant map associated with a suspension of a complexified family of boundary value problems.
Keywords: Hermitian form, spectral flow, Brouwer degree. 
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A. Portaluri. Indefinite Sturm Theory. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 91-96. http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a7/

[1] V. I. Arnold, Funkts. analiz i ego prilozhen., 19:4 (1985), 1–10 | MR | Zbl

[2] H. Edwards, Ann. of Math., 80 (1964), 2–57 | DOI | MR | Zbl

[3] T. Kato, Perturbation Theory for Linear Operators, Grundlehren der Mathematischen Wissenschaften, 132, Springer-Verlag, New York–Berlin, 1980 | MR | Zbl

[4] M. Musso, J. Pejsachowicz, A. Portaluri, Topological Methods in Nonlinear Analysis, 25:1 (2005), 69–99 | DOI | MR | Zbl

[5] M. Musso, J. Pejsachowicz, A. Portaluri, Esaim Control Optim. Calc. Var., 13:3 (2007), 598–621 | DOI | MR | Zbl

[6] V. Yu. Ovsienko, Matem. zametki, 47:3 (1990), 65–73 | MR | Zbl

[7] J. Robbin, D. Salamon, Bull. London Math. Soc., 27 (1995), 1–33 | DOI | MR | Zbl