Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-21T03:38:36.315Z Has data issue: false hasContentIssue false

On the nonexistence of L2-solutions of nth order differential equations

Published online by Cambridge University Press:  20 January 2009

M. K. Grammatikopoulos
Affiliation:
Department of MathematicsUniversity of IoanninaIoannina, Greece
M. R. Kulenović
Affiliation:
Department of MathematicsUniversity of SarajevoSarajevo, Yugoslavia
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider the equation

where is the generalised derivative of x defined as follows: for every tT

.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Burlak, J., On the nonexistence of L2-solutions of a class of nonlinear differential equations, Proc. Edinburgh Math. Soc. 14 (1965), 257268.CrossRefGoogle Scholar
(2)Coppel, W. A., Disconjugancy (Lecture notes in mathematics 220, Springer-Verlag, 1971).CrossRefGoogle Scholar
(3)Hallam, T. G., On the nonexistence of Lp-solutions of certain nonlinear differential equations, Glasgow Math. J. 8 (1967), 133138.CrossRefGoogle Scholar
(4)Hardy, G. H., J. E. Littlewood and G. Pólya, Inequalities (Cambridge University Press, 1952).Google Scholar
(5)Suyemoto, L. and Waltman, P., Extension of a theorem of A. Wintner, Proc. Amer. Math. Soc. 14 (1963), 970971.CrossRefGoogle Scholar
(6)Wintner, A., A criterion for the nonexistence of L2-solutions of a non-oscillatory differential equation, J. London Math. Soc. 25 (1950), 347351.Google Scholar
(7)Wong, J. S. W., Remarks on a theorem of A. Wintner, L'Enseignment Mathematique 13 (1967), 103106.Google Scholar
(8)Wong, J. S. W., On L2-solutions of linear ordinary differential equations, Duke Math. J. 38 (1971), 9396.CrossRefGoogle Scholar