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The Variation of Characteristic Values and Functions

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Partial Differential Equations

Part of the book series: Mathematics and Its Applications ((MAIA,volume 15))

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Abstract

The Green’s function associated with the second order equation

$$ u'' + q(x)u = 0, u (a) = u (1) = 0, $$
((1))

has been discussed. Analogous methods are used in the following chapter to obtain the Hadamard variational formula.

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Bibliography and Comments

  • R. Bellman and S. Lehman, ‘Functional Equations in the Theory of Dynamic Programming - X: Resolvents, Characteristic Functions and Values’, Duke Mathematical Journal 27 (1960), 55–70.

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  • R. Bellman and S. Lehman, ‘Functional Equations in the Theory of Dynamic Programming - IX: Variational Analysis, Analytic Continuation, and Imbedding of Operators’, Proceedings of the National Academy of Sciences 44 (1958), 905–907.

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  • R. Bellman, ‘Functional Equations in the Theory of Dynamic Programming - VII: A Partial Differential Equations for the Fredholm Resolvent’, Proceedings of the American Mathematical Society 8 (1957) 435–440.

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Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering, University of Southern California, Los Angeles, USA

    Richard Bellman

  2. Center for Applied Mathematics, The University of Georgia, Athens, Georgia, USA

    Richard Bellman & George Adomian

Authors
  1. Richard Bellman
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  2. George Adomian
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© 1985 D. Reidel Publishing Company

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Bellman, R., Adomian, G. (1985). The Variation of Characteristic Values and Functions. In: Partial Differential Equations. Mathematics and Its Applications, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5209-6_6

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  • DOI: https://doi.org/10.1007/978-94-009-5209-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8804-6

  • Online ISBN: 978-94-009-5209-6

  • eBook Packages: Springer Book Archive

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