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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References | Similar Articles | Additional Information

**[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