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Initial Value Problems in Linear Integral Operator Equations

In: Topics in Mathematical Analysis and Applications

Author

Listed:
  • L. P. Castro

    (University of Aveiro)

  • M. M. Rodrigues

    (University of Aveiro)

  • S. Saitoh

    (Institute of Reproducing Kernels)

Abstract

For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which—in particular—generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the integral equations of Lalesco–Picard, Dixon, and Tricomi types.

Suggested Citation

  • L. P. Castro & M. M. Rodrigues & S. Saitoh, 2014. "Initial Value Problems in Linear Integral Operator Equations," Springer Optimization and Its Applications, in: Themistocles M. Rassias & László Tóth (ed.), Topics in Mathematical Analysis and Applications, edition 127, pages 175-188, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-06554-0_7
    DOI: 10.1007/978-3-319-06554-0_7
    as

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