Perturbations of solutions of Stieltjes integral equations
Author:
David Lowell Lovelady
Journal:
Trans. Amer. Math. Soc. 155 (1971), 175-187
MSC:
Primary 45L05
DOI:
https://doi.org/10.1090/S0002-9947-1971-0433175-5
MathSciNet review:
0433175
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Using multiplicative integration in two ways, formulae for solutions to perturbed Stieltjes integral equations are found in terms of unperturbed solutions. These formulae are used to obtain bounds on the difference between the perturbed solution and the unperturbed solution. The formulae are also used to explicitly solve, in terms of product integrals, a linear equation subject to nonlinear interface conditions.
- [1] W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Co., Boston, Mass., 1965. MR 0190463
- [2] F. R. Gantmacher, The theory of matrices, GITTL, Moscow, 1953; English transl. Vol. 2, Chelsea, New York, 1959. MR 16, 438; MR 21 #6372c.
- [3] Burrell W. Helton, Integral equations and product integrals, Pacific J. Math. 16 (1966), 297–322. MR 188731
- [4] J. V. Herod, Multiplicative inverses of solutions for Volterra-Stieltjes integral equations, Proc. Amer. Math. Soc. 22 (1969), 650-656.
- [5] J. S. MacNerney, Integral equations and semigroups, Illinois J. Math. 7 (1963), 148–173. MR 0144179
- [6] J. S. MacNerney, A nonlinear integral operation, Illinois J. Math. 8 (1964), 621–638. MR 0167815
- [7] R. H. Martin Jr., A bound for solutions of Volterra-Stieltjes integral equations, Proc. Amer. Math. Soc. 23 (1969), 506–512. MR 247394, https://doi.org/10.1090/S0002-9939-1969-0247394-0
- [8] -, Bounds for solutions to a class of nonlinear integral equations (submitted for publication).
- [9] J. W. Neuberger, Continuous products and nonlinear integral equations, Pacific J. Math. 8 (1958), 529–549. MR 102723
- [10] Clay C. Ross Jr., On the multiplication of solutions of homogeneous linear differential systems, J. Math. Anal. Appl. 25 (1969), 266–271. MR 232988, https://doi.org/10.1016/0022-247X(69)90229-7
- [11] F. W. Stallard, Differential systems with interface conditions, Oak Ridge National Laboratory Publication #1876 (Physics) 1955.
- [12] F. W. Stallard, Functions of bounded variation as solutions of differential systems, Proc. Amer. Math. Soc. 13 (1962), 366–373. MR 138835, https://doi.org/10.1090/S0002-9939-1962-0138835-1
- [13] A. Zettl, Adjoint and self-adjoint boundary value problems with interface conditions, MRC Technical Report #827, 1967.
Retrieve articles in Transactions of the American Mathematical Society with MSC: 45L05
Retrieve articles in all journals with MSC: 45L05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1971-0433175-5
Keywords:
Perturbations,
product integrals,
bounds,
stability,
interface conditions
Article copyright:
© Copyright 1971
American Mathematical Society