Hostname: page-component-7dd5485656-frp75 Total loading time: 0 Render date: 2025-10-31T21:53:06.529Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence and uniqueness for two-point boundary value problems

Published online by Cambridge University Press:  14 November 2011

John V. Baxley  and
Sarah E. Brown
John V. Baxley
Affiliation:
Mathematics Department, Wake Forest University, Winston-Salem, North Carolina, 27109, U.S.A.
Sarah E. Brown
Affiliation:
Southern Bell Telephone Company, Charlotte, North Carolina, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Boundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 88 , Issue 3-4 , 1981 , pp. 219 - 234
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1Baxley, J. V.. Global existence and uniqueness for second-order ordinary differential equations. J. Differential Equations 23 (1977), 315–334.CrossRefGoogle Scholar
2Bebernes, J. W. and Gaines, R.. Dependence on boundary data and a generalized boundary value problem. J. Differential Equations 4 (1968), 359–368.CrossRefGoogle Scholar
3Bebernes, J. W. and Gaines, R.. A generalized two-point boundary value problem. Proc. Amer. Math. Soc. 19 (1968), 749–754.CrossRefGoogle Scholar
4Coppel, W. A.. Stability and asymptotic behavior of differential equations (Boston: Heath, 1965).Google Scholar
5Keller, H. B.. Existence theory for two-point boundary value problems. Bull. Amer. Math. Soc. 72 (1966), 728–731.CrossRefGoogle Scholar
6Keller, H. B.. Numerical methods for two-point boundary-value problems (Waltham, Mass.: Blaisdell, 1968).Google Scholar
7Muldowney, J. S. and Willett, D.. An elementary proof of the existence of solutions to second order nonlinear boundary value problems. SIAM J. Math. Anal. 5 (1974), 701–707.CrossRefGoogle Scholar
8Protter, M. H. and Weinberger, H. F.. Maximum principles in differential equations (Englewood Cliffs, N.J.: Prentice-Hall, 1967).Google Scholar