Solutions of some periodic Stieltjes integral equations

Authors:
G. W. Marrah and T. G. Proctor

Journal:
Proc. Amer. Math. Soc. **34** (1972), 121-127

MSC:
Primary 45M05

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291740-9

MathSciNet review:
0291740

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Abstract: Nonlinear periodic perturbations of a family of linear periodic Stieltjes integral equations are considered and sufficient conditions are given for the existence of a periodic solution for one member of the family. Conditions are given under which the solutions of the family approach the periodic solution asymptotically. A Floquet type theorem for periodic Stieltjes integral equations and several examples are given.

**[1]**J. K. Hale,*Oscillations in nonlinear systems*, McGraw-Hill, New York, 1963. MR**27**#401. MR**0150402 (27:401)****[2]**-,*Functional differential equations*, Springer-Verlag, New York, 1971. MR**0466837 (57:6711)****[3]**J. S. Mac Nerney,*A nonlinear integral operation*, Illinois J. Math.**8**(1964), 621-638. MR**29**#5082. MR**0167815 (29:5082)****[4]**G. W. Marrah,*Qualitative theory for Stieltjes integral equations*, Ph.D. Dissertation, Clemson University, Clemson, S.C., 1971.**[5]**R. H. Martin, Jr.,*Bounds for solutions to a class of nonlinear integral equations*, Trans. Amer. Math. Soc.**160**(1971), 131-138. MR**0283643 (44:873)****[6]**J. A. Reneke,*A variation of parameter formula*, Clemson Mathematics Department Report #87, Clemson, S.C., 1971.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0291740-9

Keywords:
Stieltjes integral equations,
order additive,
Floquet theorem,
periodic,
difference equation,
perturbation of linear ordinary differential equation

Article copyright:
© Copyright 1972
American Mathematical Society