Advertisement

Siberian Mathematical Journal

, Volume 25, Issue 1, pp 88–100 | Cite as

Variational approach to the periodic solutions problem

  • A. I. Perov
  • T. I. Smagina
  • V. L. Khatskevich
Article

Keywords

Periodic Solution Variational Approach Solution Problem Periodic Solution Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    V. A. Trenogin, “Boundary-value problems for abstract elliptic equations,” Dokl. Akad. Nauk SSSR,170, No. 6, 1028–1031 (1966).Google Scholar
  2. 2.
    G. I. Laptev, “Strongly elliptic second-order equations in a Hilbert space,” Lit. Mat. Sb.,8, 87–99 (1968).Google Scholar
  3. 3.
    S. G. Krein, Linear Differential Equations in Banach Space,” Am. Math. Soc., Providence (1971).Google Scholar
  4. 4.
    Yu. A. Dubinskii, “Periodic solutions of parabolic-elliptic equations,” Mat. Sb.,76, No. 4, 1335–1337 (1968).Google Scholar
  5. 5.
    T. I. Smagina, “On periodic boundary-value problem for second-order equations in a Hilbert space,” in: Differential Equations and Their Applications [in Russian], Mezhvuz. Sb., Tyumen (1980), pp. 117–127.Google Scholar
  6. 6.
    W. S. Loud, “Periodic solutions of nonlinear differential equations of Duffing type,” Proc. U. S., in: Japan Seminar on Differential and Functional Equations, New York (1967), pp. 120–131.Google Scholar
  7. 7.
    D. E. Leach, “On Poincare's perturbation theorem and a theorem of W. S. Loud,” J. Different. Equat., No. 7, 34–53 (1970).Google Scholar
  8. 8.
    A. C. Lazer, “Application of lemma on bilinear forms to a problem in nonlinear oscillations,” Proc. Am. Math. Soc., No. 3, 89–94 (1972).Google Scholar
  9. 9.
    R. Kannan, “Periodically perturbed conservative systems,” J. Different. Equat.,16, No. 3, 506–514 (1974).Google Scholar
  10. 10.
    A. Schair, “An existence theorem for periodically perturbed conservative systems,” Mich. Math. J.,20, No. 4, 385–392 (1974).Google Scholar
  11. 11.
    T. I. Smagina, “On the regularity classes for second-order vectorequations,” Diff. Urav.,11, No. 7, 1320–1322 (1976).Google Scholar
  12. 12.
    A. I. Perov, “Variational methods in the theory of nonlinear oscillations,” Voronezh Univ. (1981).Google Scholar
  13. 13.
    A. I. Perov, “On potential operators,” Mat. Zametki,24, No. 6, 793–799 (1978).Google Scholar
  14. 14.
    S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).Google Scholar
  15. 15.
    A. I. Perov, “On the fixed point principle with two-sided constraints,” Dokl. Akad. Nauk SSSR,124, No. 4, 756–759 (1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • A. I. Perov
  • T. I. Smagina
  • V. L. Khatskevich

There are no affiliations available

Personalised recommendations