103
Views
10
CrossRef citations to date
0
Altmetric
Regular Papers

Spectral analysis for one class of second-order indefinite non-self-adjoint differential operator pencil

Pages 1837-1849 | Received 27 Mar 2010, Accepted 07 Oct 2010, Published online: 26 Jan 2011

References

  • Deift , P and Trubowitz , E . 1979 . Inverse scattering on the line . Commun. Pure Appl. Math. , XXXII : 121 – 251 .
  • Faddeev , LD . 1964 . Properties of the S-matrix of the one-dimensional Schrodinger equation . Trudy Mat. Inst. V.A. Steklova , 73 : 314 – 336 .
  • Aktosun , T , Klaus , M and Van der Mee , C . 1998 . Wave scattering in one dimension with absorption . J. Math. Phys. , 39 : 1957 – 1992 .
  • Jaulent , M and Jean , C . 1976 . The inverse problem for the one-dimensional Schrodinger equation with an energy-dependent potential: I . Ann. Inst. H. Poincare, Sect. A , 25 : 105 – 118 .
  • Jaulent , M and Jean , C . 1976 . The inverse problem for the one-dimensional Schrodinger equation with an energy-dependent potential: II . Ann. Inst. H. Poincare, Sect. A , 25 : 119 – 137 .
  • Jaulent , M . 1976 . Inverse scattering problems in absorbing media . J. Math. Phys. , 17 : 1351 – 1360 .
  • Pivovarchik , VN . 1999 . Reconstruction of the potential of the Sturm–Liouville equation from three spectra of boundary value problems . Funct. Anal. Appl. , 33 ( 3 ) : 233 – 235 .
  • Yurko , V . 2001 . Recovery of differential equations with nonlinear dependence on the spectral parameter . Appl. Anal.: Int. J. , 78 ( 1 ) : 63 – 77 . ISSN: 1563-504X
  • Eberhard , W and Freiling , G . 1992 . The distribution of the eigenvalues for second order eigenvalue problems in the presence of an arbitrary number of turning points . Results Math. , 21 : 24 – 41 .
  • Freiling , G and Yurko , VA . 2001 . Inverse Sturm–Liouville Problems and their Applications , New York : NOVA Science .
  • Yurko , V . 2006 . Inverse spectral problems for differential pencils on the half-line with turning points . J. Math. Anal. Appl. , 320 : 439 – 463 .
  • Krein , MG . 1955 . On determination of the potential of a particle from its S-function . Rep. AS USSR , 105 ( 3 ) : 433 – 436 .
  • Blagoveshchensky , AS . 1969 . A one-dimensional inverse boundary value problem for a second order hyperbolic equation . Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , 15 : 85 – 90 . (in Russian)
  • Grinberg , NI . 1991 . The one-dimensional inverse scattering problem for the wave equation . Math. USSR Sb. , 70 : 557 – 572 . [Mat. Sb. 181 (8) (1990), pp. 1114–1129 (in Russian)]
  • Belishev , MI . 1987 . Inverse spectral indefinite problem for the equation y′′ + λ p(x) y = 0 on an interval . Funct. Anal. Appl. , 21 ( 2 ) : 68 – 69 .
  • Bethe , HA . 1940 . A continuum theory of the compound nucleus . Phys. Rev. , 57 : 1125 – 1144 .
  • Feshbach , H and Porter , CE . 1954 . Weisskopf VF Model for nuclear reactions with neutrons . Phys. Rev. , 96 : 448 – 464 .
  • Gasymov , MG . 1980 . Spectral analysis of a class non-self-adjoint operator of the second order . Funct. Anal. Appl. , 34.1 : 14 – 19 . (in Russian)
  • Pastur , LA and Tkachenko , VA . 1991 . An inverse problem for one class of one dimensional Schrodinger's operators with complex periodic potentials . MATH USSR IZV , 37 ( 3 ) : 611 – 629 .
  • Guillemin , V and Uribe , A . 1983 . Hardy functions and the inverse spectral method . Commun. Partial Differ. Eqns , 8 ( 13 ) : 1455 – 1474 .
  • Gasymov , MG and Gusejnov , GS . 1981 . Determination of diffusion operators according to spectral data . Dokl. Akad. Nauk Az. SSR , 37 ( 2 ) : 19 – 23 .
  • Efendiev , RF . 2007 . The characterization problem for one class of second order operator pencil with complex periodic coefficients . Moscow Math. J. , 7 ( 1 ) : 55 – 65 .
  • Efendiev , RF . 2006 . Complete solution of an inverse problem for one class of the high order ordinary differential operators with periodic coefficients . Zh. Mat. Fiz. Anal. Geom. , 2 ( 1 ) : 73 – 86 .
  • Efendiev , RF . 2005 . Spectral analysis of a class of non-self-adjoint differential operator pencils with a generalized function . Teoret. Mat. Fiz. , 145 ( 1 ) : 102 – 107 . (in Russian) [Theor. Math. Phys.1451(1), pp. 1457–461 (in English)]
  • Efendiev , RF . 2008 . Inverse indefinite spectral problem for second order differential operator with complex periodic coefficients . Proc. Baku State Univ. , 4 : 17 – 22 . (In Russian)
  • Borg , G . 1946 . Eine Umkehrung der Sturm–Liouvillschen eigenwertaufgabe . Acta Math. , 78 : 196
  • Gesztesy , F and Holden , H . 2003 . Soliton Equations and Their Algebro-Geometric Solutions. Vol. I: (1 + 1)-Dimensional Continuous Models, Cambridge Studies in Advanced Mathematics , Vol. 79 , Cambridge : Cambridge University Press .
  • Naimark , MA . 1969 . Linear Differential Operators , Moscow : Nauka . (in Russian)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.