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Relations Between Boundary Value Functions for a Nonlinear Differential Equation and its Variational Equations*

Published online by Cambridge University Press:  20 November 2018

James D. Spencer
James D. Spencer*
Affiliation:
Louisiana Tech University, Ruston, Louisiana 71270
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We consider here the nonlinear differential equation

(1.1)

where x ∊l= [a, ∞). We will make the following assumptions

  1. (A) f is continuous on [a, ∞) × Rn,

  2. (B) solutions of initial value problems (I.V.P.'s) are unique and extend throughout [a, ∞).

  3. (C)

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 269 - 276
Copyright
Copyright © Canadian Mathematical Society 1975

Footnotes

*

The results presented here were part of the author's Ph.D. dissertation, University of Nebraska, August, 1973. The author gratefully acknowledges the guidance of his advisor, Professor Allan C. Peterson.

References

1. Erbe, Lynn, Boundary value problems for ordinary differential equations, Rocky Mountain J. of Math. (1) 4 (1971), 707-732.Google Scholar
2. Hartman, P., Ordinary Differential Equations, John Wiley, New York (1964), (MR 30 # 1270).Google Scholar
3. Jackson, L. K., Uniqueness of solutions of boundary value problems for ordinary differential equations, SIAM J. on Applied Math. (4) 24 (1973).Google Scholar
4. Jackson, L. K. Uniqueness and existence of solutions of boundary value problems for third order differential equations, J. of Diff. Equations(3) 13 (1973).Google Scholar
5. Peterson, A. C., On a relation between a theorem of Hartman and a theorem of Sherman, Canad. Math. Bull. (2) 16 (1973).Google Scholar
6. Peterson, Dale, Uniqueness, existence, and comparison theorems for ordinary differential equations, Ph.D. thesis, University of Nebraska, 1973.Google Scholar
7. Spencer, J. D., Boundary value functions for nonlinear differential equations, J. of Differential Eqs. (to appear).Google Scholar