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2010 | 8 | 2 | 378-388
Tytuł artykułu

Basis properties of a fourth order differential operator with spectral parameter in the boundary condition

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EN
Abstrakty
EN
We consider a fourth order eigenvalue problem containing a spectral parameter both in the equation and in the boundary condition. The oscillation properties of eigenfunctions are studied and asymptotic formulae for eigenvalues and eigenfunctions are deduced. The basis properties in L p(0; l); p ∈ (1;∞); of the system of eigenfunctions are investigated.
Twórcy
Bibliografia
  • [1] Aliyev Z.S., On the defect basisity of the system of root functions of a fourth order spectral problem with spectral parameter in boundary condition, News of Baku University, Series of Phys.-Math. Sci., 2008, 4, 8–16
  • [2] Banks D., Kurowski G., A Prüfer transformation for the equation of a vibrating beam subject to axial forces, J. Differential Equations, 1977, 24, 57–74 http://dx.doi.org/10.1016/0022-0396(77)90170-X
  • [3] Ben Amara J., Fourth-order spectral problem with eigenvalue in boundary conditions, In: Kadets V., Zelasko W. (Eds), Proc. Int. Conf. Funct. Anal. and its Applications dedicated to the 110 anniversary of S. Banach (28–31 may 2002 Lviv Ukraine), North-Holland Math. Stud., Elsevier, 2004, 197, 49–58
  • [4] Ben Amara J., Sturm theory for the equation of vibrating beam, J. Math. Anal. Appl., 2009, 349, 1–9 http://dx.doi.org/10.1016/j.jmaa.2008.07.055
  • [5] Ben Amara J., Oscillation properties for the equation of vibrating beam with irreqular boundary conditions, J. Math. Anal. Appl., 2009, 360, 7–13 http://dx.doi.org/10.1016/j.jmaa.2009.05.042
  • [6] Ben Amara J., Vladimirov A.A., On oscillation of eigenfunctions of a fourth-order problem with spectral parameter in boundary condition, J. Math. Sciences, 2008, 150(5), 2317–2325 http://dx.doi.org/10.1007/s10958-008-0131-z
  • [7] Fulton C.T., Two-point boundary-value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy.Soc. Edinburgh. Sect. A, 1977, 77, 293–308
  • [8] Kapustin N.Yu., On a spectral problem arising in a mathematical model of torsional vibrations of a rod with pulleys at the ends, Differential Equations, 2005, 41(10), 1490–1492 http://dx.doi.org/10.1007/s10625-005-0303-2
  • [9] Kapustin N.Yu., Moiseev E.I., The basis property in L p of the system of eigenfunctions corresponding to two problems with a spectral parameter in the boundary condition, Differential Equations, 2000, 36(10), 1498–1501 http://dx.doi.org/10.1007/BF02757389
  • [10] Kashin B.S., Saakyan A.A., Orthogonal series, Amer. Math. Soc., Providence, Rhode Island, 1989
  • [11] Kerimov N.B., Aliyev Z.S., On oscillation properties of the eigenfunctions of a fourth-order differential operator, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Techn. Math. Sci., 2005, 25(4), 63–76
  • [12] Kerimov N.B., Aliyev Z.S., On the basis property of the system of eigenfunctions of a spectral problem with spectral parameter in the boundary condition, Differential Equations, 2007, 43(7), 905–915 http://dx.doi.org/10.1134/S0012266107070038
  • [13] Kerimov N.B., Mirzoev V.S., On the basis properties of a spectral problem with a spectral parameter in a boundary condition, Siberian Math. J., 2003, 44(5), 813–816 http://dx.doi.org/10.1023/A:1025932618953
  • [14] Meleshko S.V., Pokornyi Yu.V., On a vibrational boundary value problem, Differentsialniye Uravneniya, 1987, 23(8), 1466–1467 (in Russian)
  • [15] Moiseev E.I., Kapustin N.Yu., On the singulatities of the root space of one spectral problem with a spectral parameter in the boundary condition, Doklady Mathematics, 2000, 66(1), 14–18
  • [16] Naimark M.A., Linear differential operators, Ungar, New York, 1967
  • [17] Roseau M., Vibrations in mechanical systems. Analytical methods and applications, Springer-Verlag, Berlin, 1987
  • [18] Russakovskii E.M., Operator treatment of boundary problems with spectral parameter entering via polynomials in the boundary conditions, Funct. Anal. Appl., 1975, 9, 358–359 http://dx.doi.org/10.1007/BF01075895
  • [19] Shkalikov A.A., Boundary-value problems for ordinary differential equations with a parameter in the boundary conditions, J. Soviet Math., 1986, 33, 1311–1342 http://dx.doi.org/10.1007/BF01084754
  • [20] Timosenko S.P., Strength and vibrations of structural members, Nauka, Moscow, 1975 (in Russian)
  • [21] Tretter C., Boundary eigenvalue problems for differential equations N q = ρPη with λ-polynomial boundary conditions, J.Differential Equations, 2001, 170, 408–471 http://dx.doi.org/10.1006/jdeq.2000.3829
  • [22] Walter J., Regular eigenvalue problems with eigenparameter in the boundary conditions, Math. Zeitschrift, 1973, 133(4), 301–312 http://dx.doi.org/10.1007/BF01177870
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-010-0002-y
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