Article PDF
Avoid common mistakes on your manuscript.
Bibliography
Artem'ev, N. A., Periodic solutions of a class of partial differential equations. Izv. Akad. Nauk, SSSR Ser. Mat. 1 (1937) [Russian].
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).
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).
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]
Karp, V. N., On periodic solutions of nonlinear hyperbolic equations. Dokl. Akad. Nauk. Uzbek. SSR 5 (1953) [Russian].
Mitryakov, A. P., On periodic solutions of the nonlinear hyperbolic equation. Trudy Inst. Mat. Meh. Akad. Nauk Uzbek. SSR 7, 137–149 (1949) [Russian]
Mitryakov, A. P., On solutions of infinite systems of nonlinear integral and integro-differential equations. Trudy Uzbek. Gosudarstv. Univ. 37 (1948) [Russian].
Prodi, C., Soluzioni periodiche di equazioni alle derivate parziali di tipo iperbolico nonlineari. Annali Mat. Pura. Appl. 42, 25–49 (1956).
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].
Sokolov, C. T., On periodic solutions of a class of partial differential equations. Dokl. Akad. Nauk. Uzbek. SSR 12, 3–7 (1953) [Russian].
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.
Zabotinskii, M. E., On periodic solutions of nonlinear partial differential equations. Dokl. Akad. Nauk SSSR (N.S.) 56, 469–472 (1947) [Russian].
Author information
Authors and Affiliations
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
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00276443