An integral equation associated with linear homogeneous differential equations

A. K. Bose

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-4

Abstract:

Associated with each linear homogeneous differential equation y ( n ) = ∑ i = 0 n − 1 a i ( x ) y ( i ) of order n on the real line, there is an equivalent integral equation f ( x ) = f ( x 0 ) + ∫ x 0 x h ( u ) d u + ∫ x 0 x [ ∫ x 0 u G n − 1 ( u , v ) a 0 ( v ) f ( v ) d v ] d u which is satisfied by each solution f ( x ) of the differential equation.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:246569

DOI: 10.1155/S0161171286000509

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