Hostname: page-component-784d4fb959-splj4 Total loading time: 0 Render date: 2025-07-16T01:41:39.721Z Has data issue: false hasContentIssue false
  • English
  • Français

On the nonexistence of Lp solutions of certain nonlinear differential equations

Published online by Cambridge University Press:  18 May 2009

Thomas G. Hallam
Thomas G. Hallam
Affiliation:
Florida State UniversityTallahassee, Florida
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.

The asymptotic behavior of the solutions of ordinary nonlinear differential equations will be considered here. The growth of the solutions of a differential equation will be discussed by establishing criteria to determine when the differential equation does not possess a solution that is an element of the space Lp(0, ∞)(p ≧ 1).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 8 , Issue 2 , July 1967 , pp. 133 - 138
Copyright
Copyright © Glasgow Mathematical Journal Trust 1967

References

1.Bellman, R., Stability theory of differential equations, McGraw-Hill (New York, 1953), p. 116.Google Scholar
2.Burlak, J., On the nonexistence of L 2 solutions of a class of nonlinear differential equations, Proc. Edinburgh Math. Soc. 14 (1965), 257–268.CrossRefGoogle Scholar
3.Hartman, P., Ordinary differential equations, Wiley (New York, 1964).Google Scholar
4.Kurss, H., A limit point criterion for nonoscillatory Sturm-Liouville differential operators; to appear.Google Scholar
5.Ševelo, V. N. and Štelik, V. G., Certain problems concerning the oscillation of solutions of nonlinear nonautonomous second order equations, Soviet Math. Dokl. 4 (1963), 383–387.Google Scholar
6.Suyemoto, L. and Waltman, P., Extension of a theorem of A. Wintner, Proc. Amer. Math. Soc. 14 (1963), 970–971.CrossRefGoogle Scholar
7.Tricomi, F. G., Differential equations, Hafner (New York, 1961).Google Scholar
8.Wintner, A., A criterion for the nonexistence of (L P)-solutions of a nonoscillatory differential equation, London Math. Soc. 25 (1950), 347–351.Google Scholar