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Regular eigenvalue problems with eigenvalue parameter in the boundary condition

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References

  1. Bauer, W.F.: Modified Sturm-Liouville Systems. Quart. appl. Math.11, 273–282 (1953)

    Google Scholar 

  2. Bôcher, M.: Lecons sur les méthodes de Sturm. Paris: Gauthier-Villars 1917

    Google Scholar 

  3. Churchill, R.V.: Expansions in series of non-orthogonal functions. Bull. Amer. math. Soc.48, 143–149 (1942)

    Google Scholar 

  4. Cohen, D.S.: An integral transform associated with boundary conditions containing an eigenvalue parameter. SIAM J. appl. Math.14, 1164–1175 (1966)

    Google Scholar 

  5. Courant, R.: Über die Anwendung der Variationsrechnung in der Theorie der Eigenschwingungen und über neue Klassen von Funktionalgleichungen. Acta math.49, 1–68 (1926)

    Google Scholar 

  6. Courant, R., Hilbert, D.: Methoden der mathematischen Physik, I. Berlin: Springer 1924

    Google Scholar 

  7. Evans, W.D.: A non-self-adjoint differential operator inL 2σ [a,b). Quart. J. Math. Oxford, II. Ser.21, 371–383 (1970)

    Google Scholar 

  8. Friedman, B.: Principles and techniques of applied mathematics. New York: John Wiley & Sons 1956

    Google Scholar 

  9. Glazman, J.M.: Direct methods of qualitative spectral analysis. Jerusalem: Israel Program for Scientific Translations 1965

    Google Scholar 

  10. Greco, D.: Su un problema ai limiti per un'equazione differenziale lineare ordinaria del secondo ordine. Giorn Mat. Battaglini, IV. Ser.,78, 216–237 (1949)

    Google Scholar 

  11. Greco, D.: Gli sviluppi in serie di autosoluzioni in un problema ai limiti relativo ad un equazione differentiale lineare del secondo ordine. Giorn. Mat. Battaglini, IV. Ser.,79, 86–120 (1949)

    Google Scholar 

  12. Hartman, P.: Ordinary differential equations. New York: John Wiely & Sons 1964

    Google Scholar 

  13. Hellwig, G.: Differentialoperatoren der mathematischen Physik. Berlin-Göttingen-Heidelberg: Springer 1964

    Google Scholar 

  14. Hille, E.: Note on the preceding paper by Mr. Peek. Annals of Math.30, 270–271 (1929)

    Google Scholar 

  15. Hölder, E.: Entwicklungssätze aus der Theorie der zweiten Variation. Acta math.70, 193–242 (1939)

    Google Scholar 

  16. Iglisch, R.: Über lineare Integralgleichungen mit vom Parameter abhängigem Kern. Math. Ann.117, 129–139 (1939)

    Google Scholar 

  17. Ince, E.L.: Ordinary differential equations. New York: Dover Publications, Inc., 1956

    Google Scholar 

  18. Jörgens, K.: Lineare Integraloperatoren. Stuttgart: Teubner 1970

    Google Scholar 

  19. Kamke, E.: Differentialgleichungen, I. Leipzig: Akademische Verlagsgesellschaft Geest & Portig K-G. 1969

    Google Scholar 

  20. Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  21. Kneser, A.: Belastete Integralgleichungen. Rend. Circ. mat. Palermo, II. Ser.37, 169–197 (1914)

    Google Scholar 

  22. Langer, R.E.: Fourier's series. The genesis and evolution of a theory. Amer. math. Monthly Suppl.54, 1–86 (1947)

    Google Scholar 

  23. Manià, B.: Autovalori di nuclei dipendenti dal parametro. Ann. Scuola norm. sup. Pisa, II. Ser.,8, 89–104 (1939)

    Google Scholar 

  24. Miranda, C.: Su di un problema al contorno relativo all'equazione del calore. Rend. Sem. mat. Univ. Padova8, 1–20 (1937)

    Google Scholar 

  25. Miranda, C.: Su di una classe di equazioni integrali il cui nucleo è funzione del parametro. Rend. Circ. mat. Palermo60, 286–304 (1936)

    Google Scholar 

  26. Morgan, G.W.: Some remarks on a class of eigenvalue problems with special boundary conditions. Quart. appl. Math.11, 157–165 (1953)

    Google Scholar 

  27. Morse, M.: The calculus of variation in the large. Amer. Math. Soc. Colloquium Publications, vol. 18, 1934

  28. Neumark, M.A.: Lineare Differentialoperatoren. Berlin: Akademie-Verlag 1963

    Google Scholar 

  29. Odhnoff, J.: Operators generated by differential problems with eigenvalue parameter in equation and boundary condition. Meddel. Lunds Univ. mat. Sem.14, 1–80 (1959)

    Google Scholar 

  30. Peyerimhoff, A.: Gewöhnliche Differentialgleichungen, I und II. Frankfurt a. M.: Akademische Verlagsgesellschaft 1970

    Google Scholar 

  31. Reid, W.T.: Ordinary differential equations. New York: John Wiley & Sons, Inc., 1971

    Google Scholar 

  32. Sansone, G.: Equazioni differenziali nel campo reale, I. Bologna: Zanichelli 1956

    Google Scholar 

  33. Schäfke, F.W., Schneider, A.:S=hermitesche Rand-Eigenwertprobleme I, II, III. Math. Ann.162, 9–26 (1966);165, 236–260 (1966);177, 67–94 (1968)

    Google Scholar 

  34. Smirnov, W.J.: Lehrgang der höheren Mathematik, IV. Berlin: VEB Deutscher Verlag der Wissenschaften 1968

    Google Scholar 

  35. Tamarkin, J.D.: On Fredholm's integral equations whose kernels are analytic in a parameter. Ann. of Math. (2)28, 127–152 (1927)

    Google Scholar 

  36. Zecca, P.: Su un problema al contorno per l'equazione Δu+λu=0. Rend. Accad. Sci. fis. mat. Napoli, IV. Ser.33, 279–303 (1966)

    Google Scholar 

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  1. Institut für Mathematik der RWTH Aachen, Templergraben 55, D-5100, Aachen, Germany

    Johann Walter

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  1. Johann Walter
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Walter, J. Regular eigenvalue problems with eigenvalue parameter in the boundary condition. Math Z 133, 301–312 (1973). https://doi.org/10.1007/BF01177870

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