Skip to main content

Multiparameter problems: The last decade

  • 671 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 964)

Keywords

  • Definiteness Condition
  • Eigenfunction Expansion
  • Asymptotic Direction
  • Compact Resolvent
  • Oscillation Theorem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. F.V. ATKINSON, Multiparameter spectral theory, Bull. Amer. Math. Soc., 74 (1968), 1–27.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. F.V. ATKINSON, Multiparameter Eigenvalue Problems I: Matrices and Compact Operators, Academic Press, New York, 1972.

    MATH  Google Scholar 

  3. P.A. BINDING, Another positivity result for determinantal operators, Proc. Roy. Soc., Edinburgh, 86A (1980), 333–337.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. P.A. BINDING, Multiparameter definiteness conditions, Proc. Roy. Soc., Edinburgh, 89A (1981), 319–332.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. P.A. BINDING, Multiparameter definiteness conditions II, Proc. Roy. Soc., Edinburgh, (to appear).

    Google Scholar 

  6. P.A. BINDING, On the use of degree theory for nonlinear multiparameter eigenvalue problems, J. Math. Anal. Appl., 73, (1980), 381–391.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. P.A. BINDING, Variational methods for one and several parameter non-linear eigenvalue problems, Can. J. Math., 33 (1981), 210–228.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. P.A. BINDING and P.J. BROWNE, Positivity results for determinantal operators, Proc. Roy. Soc. Edinburgh, 81A (1978), 267–271.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. P.A. BINDING and P.J. BROWNE, A variational approach to multiparameter eigenvalue problems of matrices, S.I.A.M. J. Math. Anal., 8 (1977), 259–273.

    MathSciNet  MATH  Google Scholar 

  10. P.A. BINDING and P.J. BROWNE, A variational approach to multiparameter eigenvalue problems in Hilbert space, S.I.A.M. J. Math. Anal., 9 (1978), 1054–1067.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. P.A. BINDING and P.J. BROWNE, Comparison cones for multiparameter eigenvalue problems, J. Math. Anal. Appl., 77 (1980), 132–149.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. P.A. BINDING and P.J. BROWNE, Spectral properties of two-parameter eigenvalue problems, Proc. Roy. Soc. Edinburgh, 89A (1981), 157–173.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. P.A. BINDING, P.J. BROWNE and L. TURYN, Existence conditions for two-parameter eigenvalue problems, Proc. Roy. Soc. Edinburgh, to appear.

    Google Scholar 

  14. P.J. BROWNE, A multiparameter eigenvalue problem, J. Math. Anal. Appl., 38 (1972), 553–568.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. P.J. BROWNE, A singular multiparameter eigenvalue problem in second order ordinary differential equations, J. Differential Equations, 12, (1972), 81–94.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. P.J. BROWNE, Multiparameter spectral theory, Indiana Univ. Math. J., 24 (1974), 249–257.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. P.J. BROWNE, Multiparameter problems, Proceedings 174 Dundee Conference on Ordinary and Partial Differential Equations, Springer-Verlag Lecture Notes in Mathematics, Vol. 415, 78–84.

    Google Scholar 

  18. P.J. BROWNE, Abstract Multiparameter Theory I, J. Math. Anal. Appl. 60 (1977), 259–273.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. P.J. BROWNE, A completeness theorem for a non-linear multiparameter eigenvalue problem, J. Differential Equations, 23 (1977), 285–292.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. P.J. BROWNE, Abstract multiparameter theory II, J. Math. Anal. Appl., 60 (1977), 274–279.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. P.J. BROWNE, The interlacing of eigenvalues for periodic multiparameter problems, Proc. Roy. Soc. Edinburgh, 80A (1978), 357–362.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. P.J. BROWNE, Abstract multiparameter theory III, J. Math. Anal. Appl., 73 (1980), 561–567.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. P.J. BROWNE and B.D. SLEEMAN, Non-linear multiparameter Sturm-Liouville problems, J. Differential Equations, 34 (1979) 139–146.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. P.J. BROWNE and B.D. SLEEMAN, Stability regions for periodic multiparameter eigenvalue problems, Proc. Roy. Soc. Edinburgh, 84A (1979), 249–257.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. P.J. BROWNE and B.D. SLEEMAN, Bifurcation from eigenvalues in nonlinear multiparameter Sturm-Liouville problems, Glasgow Math. J., 21 (1980), 85–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  26. P.J. BROWNE and B.D. SLEEMAN, Non-linear multiparameter eigenvalue problems for ordinary differential equations, J. Math. Anal. Appl., 77 (1980), 425–432.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. N. DUNFORD and J.T. SCHWARTZ, Linear Operators, Part II, Wiley-Interscience, New York (1963).

    MATH  Google Scholar 

  28. M. FAIERMAN, The completeness and expansion theorems associated with the multiparameter eigenvalue problem in ordinary differential equations, J. Differential Equations, 5 (1969), 179–213.

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. M. FAIERMAN, Eigenfunction expansions associated with a two-parameter system of differential equations, Proc. Roy. Soc. Edinburgh, 81A (1978), 79–93.

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. M. FAIERMAN, An Oscillation theorem for a two-parameter system of differential equations, Quaestionnes Math., 3 (1979), 313–321.

    CrossRef  MathSciNet  MATH  Google Scholar 

  31. M. FAIERMAN, An eigenfunction expansion associated with a two parameter system of differential equations, Proc. Roy. Soc. Edinburgh 89A (1981), 143–155.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. A. KÄLLSTRÖM and B.D. SLEEMAN, A left definite multiparameter eigenvalue problem in ordinary differential equations, Proc. Roy. Soc. Edinburgh, 74A (1974/5), 145–155.

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. A. KÄLLSTRÖM and B.D. SLEEMAN, Multiparameter spectral theory, Ark. für Mat., 15 (1977), 93–99.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. B.D. SLEEMAN, Multiparameter Spectral Theory in Hilbert Space, Pitman, London,(1978).

    MATH  Google Scholar 

  35. B.D. SLEEMAN, Singular linear differential operators with many parameters, Proc. Roy. Soc. Edinburgh, 71A (1973), 199–232.

    MathSciNet  MATH  Google Scholar 

  36. L. TURYN, Sturm-Liouville problems with several parameters, J. Differential Equations, 38 (1980), 239–259.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Additional information

Dedicated to Richard Guy on the occasion of his 65th birthday

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Browne, P.J. (1982). Multiparameter problems: The last decade. In: Everitt, W., Sleeman, B. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 964. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064991

Download citation

  • DOI: https://doi.org/10.1007/BFb0064991

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11968-5

  • Online ISBN: 978-3-540-39561-4

  • eBook Packages: Springer Book Archive