SOME ANALOGUES OF A THEOREM OF PEANO FOR BOUNDARY VALUE PROBLEM

Authors

  • RICK BRANTLEY Department of Algebra, Combinatorics, and Analysis Auburn University Auburn, Alabama 36849 USA.
  • JOHNNY HENDERSON Department of Algebra, Combinatorics, and Analysis Auburn University Auburn, Alabama 36849 USA.

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4577

Keywords:

theorem of Peano, boundary value problems

Abstract

Under certain conditions, solutions of boundary value problems for $y'''=f (x,y, y', y'')$ are differentiated with respect to boundary conditions, both boundary points and boundary values. The results obtained are analogues of one of Peano's theorems on initial value problems.

References

G. A. Bliss, Lectures on the Calculus of Variations, University of Chicago Press, Chicago, 1946.

D. Hankerson, Boundary Value Problems for n-th order difference equations, Ph.D. dissertation, University of Nebraska, Lincoln, Nebraska, 1986.

P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.

J. Henderson, "Right focal point boundary value problems for ordinary differential equations and variational equations", J. Math. Anal. Appl.-98 (1984), 363-377.

J. Henderson, "Right (m1; ... ;mt) focal boundary value problems for third-order differential equations", J. Math. Phys. Sci. 18 (1984), 405-413.

J. Henderson, "Disconjugacy, disfocality, and differentiation with respect to boundary conditions", J. Math. Anal. Appl. 121 (1987), 1-9.

L. Jackson, "Uniqueness of solutions of boundary value problems for ordinary differential equations", SIAM J. Math. Appl. 24 (1973), 535-538.

A. Peterson, "An expression for the first conjugate point for an nth order nonlinear differential equation", Proc. Amer. Math. Soc. 61 (1976), 300-304.

A. Peterson, "Comparison theorems and existence theorems for ordinary differential equations", J. Math. Anal. Appl. 55 (1976), 773-784.

A. Peterson, "Existence-uniqueness for ordinary differential equations", J. Math. Anal. Appl. 64 (1978), 166-172.

A. Peterson,"Existence-uniqueness for focal-point boundary value problems", SIAM J. Math. Anal. 12 (1981), 173-185.

A. Peterson, "Existence and uniqueness theorems for nonlinear difference equations", J. Math. Anal. Appl. 125 (1987), 185-191.

J. Spencer, "Relations between boundary value functions for a nonlinear differential equation and its variational ·equations", Canad. Math. Bull. 18 (1975), 269-276.

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Published

1991-03-01

How to Cite

BRANTLEY, R., & HENDERSON, J. (1991). SOME ANALOGUES OF A THEOREM OF PEANO FOR BOUNDARY VALUE PROBLEM. Tamkang Journal of Mathematics, 22(1), 83–98. https://doi.org/10.5556/j.tkjm.22.1991.4577

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