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Application of Liapunov theory to boundary value problems. II


Authors: J. H. George and R. J. York
Journal: Proc. Amer. Math. Soc. 37 (1973), 207-212
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1973-0313568-4
MathSciNet review: 0313568
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Abstract: The second order vector differential equation $ x'' = f(t,x,x')$ is considered. Liapunov conditions for existence of solutions to boundary value problems are obtained strictly in terms of the function f, extending the results of George and Sutton [1].


References [Enhancements On Off] (What's this?)

  • [1] J. H. George and W. G. Sutton, Application of Liapunov theory to boundary value problems, Proc. Amer. Math. Soc. 25 (1970), 666-671. MR 41 #5725. MR 0261106 (41:5725)
  • [2] P. Hartman, Ordinary differential equations, Wiley, New York, 1964. MR 30 #1270. MR 0171038 (30:1270)
  • [3] H. W. Knobloch, On the existence of periodic solutions for second order vector differential equations, J. Differential Equations 9 (1971), 67-85. MR 43 #3557. MR 0277824 (43:3557)

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DOI: https://doi.org/10.1090/S0002-9939-1973-0313568-4
Keywords: Boundary value problems, Liapunov theory, existence, uniqueness
Article copyright: © Copyright 1973 American Mathematical Society

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