Linear ordinary differential equations with Laplace-Stieltjes transforms as coefficients

Author:
James D’Archangelo

Journal:
Trans. Amer. Math. Soc. **195** (1974), 115-145

MSC:
Primary 34A30

MathSciNet review:
0344563

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Abstract: The *n*-dimensional differential system is considered, where *R* is a constant complex matrix and is an matrix whose entries are complex valued functions which are representable as absolutely convergent Laplace-Stieltjes transforms, , for . The determining functions, , are C valued, locally of bounded variation on , continuous from the right, and . Sufficient conditions on the determining functions are found which assure the existence of solutions of certain specified forms involving absolutely convergent Laplace-Stieltjes transforms for and which behave asymptotically like certain solutions of the nonperturbed equation . Analogous results are proved for the *n*th order equation , where and the are like above for .

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0344563-2

Keywords:
*n*-dimensional system,
Laplace-Stieltjes transforms,
determining functions,
locally of bounded variation,
absolutely convergent integrals,
asymptotic behavior,
regular singular point theory,
majorant equation,
Jordan canonical form,
contraction principle,
absolutely continuous,
completely monotone solutions,
successive approximations,
Fourier transforms,
geometric relation of roots,
uniformly almost periodic functions,
Fourier expansions,
*n*th order equation

Article copyright:
© Copyright 1974
American Mathematical Society