Geodesic
Spectral estimates for fourth-order differential operator with periodic coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 86-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a self-adjoint fourth-order operator on the unit interval with real 1-periodic coefficients and Neumann–Dirichlet type boundary conditions. We determine eigenvalue asymptotics at high energy.
Keywords: spectrum, fourth-order differential operator, eigenvalue asymptotics, fundamental matrix. 
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D. M. Polyakov. Spectral estimates for fourth-order differential operator with periodic coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2022), pp. 86-92. http://geodesic.mathdoc.fr/item/IVM_2022_7_a8/

[1] Kitavtsev G., Recke L., Wagner B., “Asymptotics for the spectrum of a thin film equation in a singular limit”, Siam. J. Appl. Dyn. Syst., 11:4 (2012), 1425–1457 | DOI | MR | Zbl

[2] Laugesen R. S., Pugh M. C., “Linear stability of steady states for thin film and Cahn-Hilliard type equations”, Arch. Ration. Mech. Anal., 154 (2000), 3–51 | DOI | MR | Zbl

[3] Caudill Jr L.F., Perry P. A., Schueller A. W., “Isospectral sets for fourth-order ordinary differential operators”, SIAM J. Math. Anal., 29:4 (1998), 935–966 | DOI | MR | Zbl

[4] McLaughlin J. R., “An inverse eigenvalue problem of order four”, SIAM J. Math. Anal., 7:5 (1976), 646–661 | DOI | MR | Zbl

[5] Badanin A., Korotyaev E., “Trace formula for fourth order operators on the circle”, Dynamics of PDE, 10:4 (2013), 343–352 | MR | Zbl

[6] Badanin A., Korotyaev E., “Trace formula for fourth order operators on unit interval. II”, Dynamics of PDE, 12:3 (2015), 217–239 | MR | Zbl

[7] Polyakov D. M., “Spektralnyi analiz nesamosopryazhennogo operatora chetvertogo poryadka s negladkimi koeffitsientami”, Sib. matem. zhurn., 56:1 (2015), 165–184 | MR | Zbl

[8] Badanin A. V., Korotyaev E. L., “Spektralnye otsenki dlya periodicheskogo operatora chetvertogo poryadka”, Algebra i analiz, 22:5 (2010), 1–48 | MR

[9] Gunes H., Kerimov N. B., Kaya U., “Spectral properties of fourth order differential operators with periodic and antiperiodic boundary conditions”, Results Math., 68 (2015), 501–518 | DOI | MR | Zbl

[10] Polyakov D. M., “Spektralnyi analiz differentsialnogo operatora chetvertogo poryadka s periodicheskimi i antiperiodicheskimi kraevymi usloviyami”, Algebra i analiz, 27:5 (2015), 117–152

[11] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[12] Badanin A., Korotyaev E., “Third order operators with three-point conditions associated with Boussinesq's equation”, Appl. Anal., 100 (2021), 527–560 | DOI | MR | Zbl