Skip to main content Accessibility help
×
Home

Solution Space Decompositions for nth Order Linear Differential Equations

  • G. B. Gustafson (a1) and S. Sedziwy (a1)

Extract

Consider the wth order scalar ordinary differential equation

with pr ∈ C([0, ∞) → R ) . The purpose of this paper is to establish the following:

DECOMPOSITION THEOREM. The solution space X of (1.1) has a direct sum Decomposition

where M1 and M2 are subspaces of X such that

(1) each solution in M1\﹛0﹜ is nonzero for sufficiently large t ﹛nono sdilatory) ;

(2) each solution in M2 has infinitely many zeros ﹛oscillatory).

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Solution Space Decompositions for nth Order Linear Differential Equations
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Solution Space Decompositions for nth Order Linear Differential Equations
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Solution Space Decompositions for nth Order Linear Differential Equations
      Available formats
      ×

Copyright

References

Hide All
1. Dolan, J. M., On the relationship between a linear third order equation and its adjoint, J. Differential Equations 7 (1970), 367388.
2. Dolan, J. M. and Klaasen, G. A., Strongly oscillatory and nonoscillatory subspaces of linear equations, Can. J. Math. 27 (1975), 106110.
3. Dunford, N. and Schwartz, J. T., Linear operators, part I: general theory (Interscience, New York, 1958).
4. Gustafson, G. B., Higher order separation and comparison theorems, with applications to solution space problems, Ann. Mat. Pura Appl. 95 (1973), 245254.
5. Gustafson, G. B., The nonequivalence of oscillation and nondisconjugacy, Proc. Amer. Math. Soc. 25 (1970), 254260.
6. Neuman, F., On two problems on oscillations of linear differential equations of the third order, preprint (Brno, Czechoslovakia), to appear.
7. Krasnoselskii, M. A., Positive solutions of operator equations (P. Noordhoof Ltd., Groningen, The Netherlands, 1964).
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Solution Space Decompositions for nth Order Linear Differential Equations

  • G. B. Gustafson (a1) and S. Sedziwy (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed