Skip to main content

Multiparameter problems: The last decade

  • Conference paper
  • First Online:
Ordinary and Partial Differential Equations

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

  • 715 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • 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

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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

W.N. Everitt B.D. Sleeman

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

Publish with us

Policies and ethics