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

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]**Jack K. Hale,*Oscillations in nonlinear systems*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR**0150402****[2]**Jack K. Hale,*Functional differential equations*, Springer-Verlag New York, New York-Heidelberg, 1971. Applied Mathematical Sciences, Vol. 3. MR**0466837****[3]**J. S. MacNerney,*A nonlinear integral operation*, Illinois J. Math.**8**(1964), 621–638. MR**0167815****[4]**G. W. Marrah,*Qualitative theory for Stieltjes integral equations*, Ph.D. Dissertation, Clemson University, Clemson, S.C., 1971.**[5]**Robert H. Martin Jr.,*Bounds for solutions to a class of nonlinear integral equations*, Trans. Amer. Math. Soc.**160**(1971), 131–138. MR**0283643**, 10.1090/S0002-9947-1971-0283643-4**[6]**J. A. Reneke,*A variation of parameter formula*, Clemson Mathematics Department Report #87, Clemson, S.C., 1971.

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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