Skip to main content
SpringerLink
Log in

Existence in the large of periodic solutions of hyperbolic partial differential equations

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  1. Artem'ev, N. A., Periodic solutions of a class of partial differential equations. Izv. Akad. Nauk, SSSR Ser. Mat. 1 (1937) [Russian].

  2. Cesari, L., (a) Periodic solutions of hyperbolic partial differential equations. Intern. Symp. of Nonlinear Differential Equations and Nonlinear Mechanics (Colorado Springs, 1961). Academic Press 1963; 33–57; Intern. Symp. on Nonlinear Oscillations (Kiev. 1961). Izdat. Akad. Nauk, SSSR 2, 440–457 (1963); —(b) A criterion for the existence in a strip of periodic solutions of hyperbolic partial differential equations (to appear).

  3. Fleischman, B. A., & F. A. Ficken, Initial value and time periodic solutions for a nonlinear wave equation. Comm. Pure Appl. Math. 10, 331–356 (1957).

    Google Scholar 

  4. Karp, V. N., Application of the wave-region method to the problem of forced nonlinear periodic vibrations of a string. Izv. Vyss. Vc. Zaved. Mat. 6 (25), 51–59 (1961) [Russian]

    Google Scholar 

  5. Karp, V. N., On periodic solutions of nonlinear hyperbolic equations. Dokl. Akad. Nauk. Uzbek. SSR 5 (1953) [Russian].

  6. Mitryakov, A. P., On periodic solutions of the nonlinear hyperbolic equation. Trudy Inst. Mat. Meh. Akad. Nauk Uzbek. SSR 7, 137–149 (1949) [Russian]

    Google Scholar 

  7. Mitryakov, A. P., On solutions of infinite systems of nonlinear integral and integro-differential equations. Trudy Uzbek. Gosudarstv. Univ. 37 (1948) [Russian].

  8. Prodi, C., Soluzioni periodiche di equazioni alle derivate parziali di tipo iperbolico nonlineari. Annali Mat. Pura. Appl. 42, 25–49 (1956).

    Google Scholar 

  9. Solov'ev, P. V., Some remarks on periodic solutions of the nonlinear equation of hyperbolic type. Izv. Akad. Nauk. SSSR, Ser. Mat. 2, 150–164 (1939) [Russian].

    Google Scholar 

  10. Sokolov, C. T., On periodic solutions of a class of partial differential equations. Dokl. Akad. Nauk. Uzbek. SSR 12, 3–7 (1953) [Russian].

    Google Scholar 

  11. Vejvoda, O., Nonlinear boundary-value problems for differential equations. Proc. Conference Differential Equations and Their Applications (Prague 1962). Prague: Publishing House Czechosl. Acad. Sci. 1963, 199–215.

    Google Scholar 

  12. Zabotinskii, M. E., On periodic solutions of nonlinear partial differential equations. Dokl. Akad. Nauk SSSR (N.S.) 56, 469–472 (1947) [Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Michigan, Ann Arbor, Michigan

    Lamberto Cesari

Authors
  1. Lamberto Cesari
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The research reported here was supported in part by U. S. National Science Foundation grant G-57 at the University of Michigan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cesari, L. Existence in the large of periodic solutions of hyperbolic partial differential equations. Arch. Rational Mech. Anal. 20, 170–190 (1965). https://doi.org/10.1007/BF00276443

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00276443

Keywords

Search

Navigation