# Article

 Title: A linear and weakly nonlinear equation of a beam: the boundary-value problem for free extremities and its periodic solutions (English) Author: Krylová, Naděžda Author: Vejvoda, Otto Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 21 Issue: 4 Year: 1971 Pages: 535-566 Summary lang: English . Category: math . MSC: 35.12 MSC: 42.00 idZBL: Zbl 0226.35008 idMR: MR0289918 DOI: 10.21136/CMJ.1971.101055 . Date available: 2008-06-09T13:53:40Z Last updated: 2020-07-28 Stable URL: http://hdl.handle.net/10338.dmlcz/101055 . Reference: [1] N. Krylová О. Vejvoda: Periodic solutions to partial diff. equations, especially to a biharmonic wave equation.Atti del Convegno sui problemi di evoluzione. Maggio, 1970. Roma. Reference: [2] W. S. Hall: On the Existence of Periodic solutions for the Equations $D_{tt} u + (- 1)^p D^{2p}_x u = \varepsilon f(., ., m)$.Journal of Differential Equations, Vol. 7, No 3 May 1970, 509-526. MR 0265738, 10.1016/0022-0396(70)90098-7 Reference: [3] W. S. Hall: Periodic Solutions of a class of Weakly Nonlinear Evolution Equations.Archive for Rational Mechanics and Analysis, Vol. 39, N. 4, 1970, 294-322. Zbl 0211.12704, MR 0274914, 10.1007/BF00281367 Reference: [4] H. Petceltová: Periodic solutions of the equation $u_{tt} + u_{xxxx} = \varepsilon f(., ., u)$.to appear. Reference: [5] O. Vejvoda: Periodic solutions of a linear and weakly nonlinear wave equation in one dimension.I, Czech. Math. J., 14 (89), 1964, 341-382. MR 0174872 Reference: [6] D. Ch. Karimov: On the periodical solutions of nonlinear equations of the fourth order.Dokl. Akad. Nauk SSSR, 49 (1945), 618-621. MR 0016195 Reference: [7] D. Ch. Karimov: On the periodical solutions of nonlinear equations of the fourth order.(Russian), Dokl. Akad. Nauk SSSR, 57 (1947), 651-653. MR 0022649 Reference: [8] D. Ch. Karimov: On the periodical solutions of nonlinear equations of the fourth order.(Russian), Dokl. Akad. Nauk Uz. SSR, 1949, No 8, 3-7. MR 0057418 Reference: [9] A. P. Mitrjakov: On the periodic solution of nonlinear partial differential equations of higher order.(Russian), Trudy Uzb. Gos. Univ., 1956, No 65, 31 - 44. Reference: [10] P. V. Solovieff: Sur les solutions périodique de certaines équations non-linéaires du quatrième ordre.Dokl. Akad. Nauk SSSR, 25 (1939), 731-734. MR 0001892 .

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