Bounds for solutions of perturbed differential equations
HTML articles powered by AMS MathViewer
- by T. G. Proctor PDF
- Proc. Amer. Math. Soc. 45 (1974), 73-79 Request permission
Abstract:
A modified form of the Alekseev variation of constants equation is used to relate the solutions of systems of the form $\dot x = f(t,x,\lambda ),\lambda$ in ${R^m}$ and the perturbed system $\dot y = f(t,y,\psi (t)) + g(t,y)$. Hypotheses are given on the $m$ parameter family of differential equations $\dot x = f(t,x,\lambda )$ so that if $\dot \psi$ and $g$ are perturbation functions, bounds can be calculated for the solutions of the perturbed system.References
- V. M. Alekseev, An estimate for the perturbations of the solutions of ordinary differential equations, Vestnik Moskov. Univ. Ser. I Mat. Meh. 2 (1961), 28–36 (Russian, with English summary). MR 0125293
- Fred Brauer, Perturbations of nonlinear systems of differential equations, J. Math. Anal. Appl. 14 (1966), 198–206. MR 192132, DOI 10.1016/0022-247X(66)90021-7
- W. A. Coppel, Stability and asymptotic behavior of differential equations, D. C. Heath and Company, Boston, Mass., 1965. MR 0190463
- R. E. Fennell and T. G. Proctor, Perturbations of nonlinear differential equations, Trans. Amer. Math. Soc. 185 (1973), 401–411. MR 361309, DOI 10.1090/S0002-9947-1973-0361309-1
- Richard K. Miller, Nonlinear Volterra integral equations, Mathematics Lecture Note Series, W. A. Benjamin, Inc., Menlo Park, Calif., 1971. MR 0511193
- B. Noble, The numerical solution of nonlinear integral equations and related topics, Nonlinear Integral Equations (Proc. Advanced Seminar Conducted by Math. Research Center, U.S. Army, Univ. Wisconsin, Madison, Wis., 1963) Univ. Wisconsin Press, Madison, Wis., 1964, pp. 215–318. MR 0173369
- J. A. Nohel, Some problems in nonlinear Volterra integral equations, Bull. Amer. Math. Soc. 68 (1962), 323–329. MR 145307, DOI 10.1090/S0002-9904-1962-10790-3
- T. G. Proctor, Periodic solutions for perturbed differential equations, J. Math. Anal. Appl. 47 (1974), 310–323. MR 432982, DOI 10.1016/0022-247X(74)90024-9
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 45 (1974), 73-79
- MSC: Primary 34D10; Secondary 34A10
- DOI: https://doi.org/10.1090/S0002-9939-1974-0344615-2
- MathSciNet review: 0344615