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On a Simple Type of Integro-differential Equation

Published online by Cambridge University Press:  20 January 2009

R. P. Gillespie
R. P. Gillespie
Affiliation:
Glasgow University
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In a previous paper in these Proceedings the author discussed conditions for a maximum or minimum of functions of integrals of the type

using the methods of the Calculus of Variations. In the effort to establish a third necessary condition for a minimum—the analogue of Jacobi's condition in the ordinary variational problem—it was found that the analogue of Jacobi's Equation was an integrodifferential equation of the form

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 2 , January 1935 , pp. 80 - 84
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

page 80 note 1 Gillespie, R. P.Pioc. Edinburgh Math. Soc. (2), 3 (1932), 87–98.CrossRefGoogle Scholar

page 80 note 2 CfBolza, O.Vorlesungen über Variationsrechnung (1909), 68–87.Google Scholar