Periodic solutions for perturbed nonlinear differential equations. II.

Proctor, T. G.

doi:10.1090/S0002-9939-1972-0289866-9

Periodic solutions for perturbed nonlinear differential equations. II.
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by T. G. Proctor

Proc. Amer. Math. Soc. 31 (1972), 219-224

DOI: https://doi.org/10.1090/S0002-9939-1972-0289866-9

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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

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 219-224
DOI: https://doi.org/10.1090/S0002-9939-1972-0289866-9
MathSciNet review: 0289866