Publication Cover
Applicable Analysis
An International Journal
Volume 78, 2001 - Issue 1-2
20
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Recovery of differential equations with nonlinear dependence on the spectral parameter

Pages 63-77 | Received 01 Oct 1999, Published online: 02 May 2007

References

  • Tamarkin , J.D. 1971 . On some of the theory of ordinary linear differential equations . Petrograd ,
  • Keldysh , M.V. 1951 . On eigenvalues and eigenfunctions of some classes of nonselfadjoint equations . Dokl. Akad. Nauk SSSR , 77 : 11 – 14 .
  • Shaklikov , A.A. 1981 . On the basis property of the eigenvectors of quadratic operators pencils . Mat. zametki , 30 ( 3 ) : 371 – 385 .
  • Shakalikov , A.A. 1983 . Selfadjoint quadratic operator pencils and elliptic problems . Funkt. Anal. i Prilozhen , 17 ( 2 ) : 38 – 61 .
  • Freiling , G. 1986 . necessary conditions for the L2-convergence of series in eigenfunctions of irregular eigenvalue problems . J. Math. Anal. Appl , 114 : 503 – 511 .
  • Freiling , G. 1988 . On the completeness and minimality of the derived chains of eigen and associated functions of boundary eigenvalue problems nonlinearly Independent on the parameter . Results in Math , 14 : 64 – 83 .
  • Freiling , G. 1990 . Multiple expansion in series of eifen-and associated functions of boundary eigenvlue problems nonlinearly dependent on the parameter . Parts I,II. Results in Math , 17 : 241 – 255 .
  • Levitan , B.M. and Sargsjan , I.S. 1975 . Introduction to Spectral Theory . AMS Transl. of Math. Monographs , 39 English translation
  • Marchenko , V.A. 1986 . Sturm-Liouville operators and their applications . Naukova Dumka English transl
  • Levitan , B.M. “ Inverse Strum-Liouville problems ” . English transl Utrecht
  • Yurko , V.A. 1992 . Recovery of nonselfadjoint differential operators on the half-line from the Weyl matrix . Math. sbornik , 72 ( 2 ) : 413 – 438 . 182, No. 3 (1991), 431-456 English transl. in Math. USSr sbornik
  • Yurko , V.A. 1999 . “ Inverse spectral problems for Differential Operators and their Applications ” . New York : Gordon and Breach .
  • Gasymov , M.G. and Gusejnov , G.S. 1981 . Determination of diffusion operators according to spectral data . Dokl. Akad. Nauk Az. SSR , 37 ( 2 ) : 19 – 23 .
  • Yurko , V.A. 1984 . Boundary value problems with a parameter in the boundary conditions . Izv. Akad. Naku Armyan. SSR, Ser. Mat , 19 ( 5 ) : 398 – 409 . English transl. in soviet J. Contemporary Math. Anal., 19, No. 5 (1984), 62-73
  • Yurko , V.A. 1997 . An inverse problem for systems of differntial equations with nonlinear dependence on the spectral parameter . Diff. Uravneniya , 33 ( 3 ) : 390 – 395 . English transl. in Diff Equations. 33 No. 3 (1997), 388-394
  • Yaammoto , M. 1990 . Inverse cigenvlaue problem for a viberation of a string with viscous drag . J.Math. Anal. Appl , 152 ( 1 ) : 20 – 34 .
  • Romanov , V.G. 1987 . “ Inverse problems in Mathematical Physics ” . Nauka , Moscow : VNU Science Press . 1984 English transl Utrecht
  • Romanov , V.G. 1994 . Inverse problems for Maxwell's equations . Inverse and Ill-posed problems for partial series. , VSP, Utrecht
  • Isakov , V. 1998 . Inverse problems or Parital Differential equations .
  • Kirsch , A. 1996 . An Introdiction to the Mathematical Theory of Unverse Problems . Applied Mathematical Sciences , 120

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.