Periodic solutions for perturbed nonlinear differential equations. II.
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- by T. G. Proctor PDF
- Proc. Amer. Math. Soc. 31 (1972), 219-224 Request permission
Abstract:
The existence of periodic solutions of the periodic system $\dot x = \varepsilon g(t,x,y,\varepsilon ),\dot y = f(t,y) + \varepsilon h(t,x,y,\varepsilon )$ is established for small $\varepsilon$ when the solution of the initial value problem $\dot y = f(t,y),y(\tau ) = \gamma$ is known and some algebraic and smoothness conditions are satisfied.References
- Lamberto Cesari, Asymptotic behavior and stability problems in ordinary differential equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 16, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959. MR 0118904
- Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402
- T. G. Proctor, Periodic solutions for perturbed nonlinear differential equations, Proc. Amer. Math. Soc. 24 (1970), 815–819. MR 255921, DOI 10.1090/S0002-9939-1970-0255921-0
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 219-224
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289866-9
- MathSciNet review: 0289866