On the monotonicity of the period function of some second order equations

Shui-Nee Chow; Duo Wang

Časopis pro pěstování matematiky (1986)

  • Volume: 111, Issue: 1, page 14-25
  • ISSN: 0528-2195

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Chow, Shui-Nee, and Wang, Duo. "On the monotonicity of the period function of some second order equations." Časopis pro pěstování matematiky 111.1 (1986): 14-25. <http://eudml.org/doc/21626>.

@article{Chow1986,
author = {Chow, Shui-Nee, Wang, Duo},
journal = {Časopis pro pěstování matematiky},
keywords = {monotonicity of the period functions; scalar equation},
language = {eng},
number = {1},
pages = {14-25},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {On the monotonicity of the period function of some second order equations},
url = {http://eudml.org/doc/21626},
volume = {111},
year = {1986},
}

TY - JOUR
AU - Chow, Shui-Nee
AU - Wang, Duo
TI - On the monotonicity of the period function of some second order equations
JO - Časopis pro pěstování matematiky
PY - 1986
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 111
IS - 1
SP - 14
EP - 25
LA - eng
KW - monotonicity of the period functions; scalar equation
UR - http://eudml.org/doc/21626
ER -

References

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  1. V. I. Arnold, Geometric Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, N.Y., 1983. (1983) MR0695786
  2. J. Carry S.-N. Chow, J. K. Hale, Abelian integrals and bifurcation theory, J. Diff. Eqn., 59(1985), 413-436. (1985) MR0807855
  3. S.-N. Chow, J. K. Hale, Methods of Bifurcation Theory, Springer-Verlag, N.Y., 1982. (1982) Zbl0487.47039MR0660633
  4. S.-N. Chow, J. A. Sanders, On the number of critical points of the period, to appear. Zbl0594.34028MR0849664
  5. W. S. Loud, Periodic solution of x" + cx + g(x) = ε f(t), Mem. Amer. Math. Soc., No. 31 (1959), 1-57. (1959) Zbl0085.30701MR0107058
  6. C. Obi, Analytical theory of nonlinear oscillation, VII, The periods of the periodic solutions of the equation x" + g(x) = 0, J. Math. Anal. Appl. 55 (1976), 295-301. (1976) Zbl0359.34038MR0460796
  7. Z. Opial, Sur les periodes des solutions de Pequation differentielle x" + g(x) - 0, Ann. Pol. Math. 10 (1961), 49-72. (1961) MR0121544
  8. R. Schaaf, Global behavior of solution branches for some Neumann problems depending on one or several parameters, to appear. Zbl0513.34033MR0727393
  9. D. Wang, On the existence of 2π-periodic solutions of differential equation x" + g(x) = p(t), Chin. Ann. Math., 5A(1) (1984), 61-72. (1984) MR0743783

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