Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A new sufficient condition for periodic solutions of weakly nonlinear differential systems


Authors: L. Cesari and J. K. Hale
Journal: Proc. Amer. Math. Soc. 8 (1957), 757-764
MSC: Primary 34.0X
MathSciNet review: 0086209
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  • [1] Lamberto Cesari, Sulla stabilità delle soluzioni dei sistemi di equazioni differenziali lineari a coefficienti periodici, Atti Accad. Italia. Mem. Cl. Sci. Fis. Mat. Nat. (6) 11 (1940), 633–695 (Italian). MR 0004660
  • [2] Lamberto Cesari and Jack K. Hale, Second order linear differential systems with periodic 𝐿-integrable coefficients, Riv. Mat. Univ. Parma 5 (1954), 55–61; errata 6 (1955), 159. MR 0071590
  • [3] E. A. Coddington and N. Levinson, Perturbations of linear systems with constant coefficients possessing periodic solutions, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, 1952, pp. 19–35. MR 0054803
  • [4] Robert A. Gambill, Stability criteria for linear differential systems with periodic coefficients, Riv. Mat. Univ. Parma 5 (1954), 169–181. MR 0070797
  • [5] Robert A. Gambill, Criteria for parametric instability for linear differential systems with periodic coefficients, Riv. Mat. Univ. Parma 6 (1955), 37–43. MR 0076120
  • [6] Robert A. Gambill and Jack K. Hale, Subharmonic and ultraharmonic solutions for weakly non-linear systems, J. Rational Mech. Anal. 5 (1956), 353–394. MR 0077741
  • [7] Jack K. Hale, Evaluations concerning products of exponential and periodic functions, Riv. Mat. Univ. Parma 5 (1954), 63–81. MR 0070758
  • [8] Jack K. Hale, On boundedness of the solutions of linear differential systems with periodic coefficients, Riv. Mat. Univ. Parma 5 (1954), 137–167. MR 0070796
  • [9] Jack K. Hale, Periodic solutions of non-linear systems of differential equations, Riv. Mat. Univ. Parma 5 (1954), 281–311. MR 0077751

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DOI: http://dx.doi.org/10.1090/S0002-9939-1957-0086209-2
Article copyright: © Copyright 1957 American Mathematical Society