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 | References | Similar Articles | Additional Information
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.
- Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402
- Jack K. Hale, Functional differential equations, Springer-Verlag New York, New York-Heidelberg, 1971. Applied Mathematical Sciences, Vol. 3. MR 0466837
- J. S. MacNerney, A nonlinear integral operation, Illinois J. Math. 8 (1964), 621–638. MR 167815 G. W. Marrah, Qualitative theory for Stieltjes integral equations, Ph.D. Dissertation, Clemson University, Clemson, S.C., 1971.
- Robert H. Martin Jr., Bounds for solutions to a class of nonlinear integral equations, Trans. Amer. Math. Soc. 160 (1971), 131–138. MR 283643, DOI https://doi.org/10.1090/S0002-9947-1971-0283643-4 J. A. Reneke, A variation of parameter formula, Clemson Mathematics Department Report #87, Clemson, S.C., 1971.
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Additional Information
Keywords:
Stieltjes integral equations,
order additive,
Floquet theorem,
periodic,
difference equation,
perturbation of linear ordinary differential equation
Article copyright:
© Copyright 1972
American Mathematical Society
