Petzeltová, Hana Application of Moser’s method to a certain type of evolution equations. (English) Zbl 0547.35081 Czech. Math. J. 33(108), 427-434 (1983). The author constructs periodic solutions of a nonlinear damped equation similar to a wave equation where the nonlinearity occurs in the highest derivatives but the nonlinear term is multiplied by a small parameter. She does this by using the Nash-Moser theory to reduce the problem to a one-dimensional problem. She obtains a useful lemma for verifying the assumptions of the Nash-Moser theory. Reviewer: E.Dancer Cited in 5 Documents MSC: 35L75 Higher-order nonlinear hyperbolic equations 35B32 Bifurcations in context of PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application Keywords:evolution equations; bifurcation equation; periodic solutions; nonlinear damped equation; Nash-Moser theory × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Moser J.: A rapidly convergent iteration method and non-linear partial differential equations. I, Ann. Scuola Norm. Sup. Pisa, Ser. 3, Vol. 20, 1966, pp. 265-315. · Zbl 0144.18202 [2] Rabinowitz P. H.: Periodic solutions of nonlinear hyperbolic partial differential equations II. Comm. Pure Appl. Math., Vol. 20, 1969, pp. 15-39. · Zbl 0157.17301 · doi:10.1002/cpa.3160220103 [3] Nirenberg L.: On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, Ser. 3, Vol. 13, 1959, pp. 116-162. · Zbl 0088.07601 [4] Pták V.: A modification of Newton’s method. Čas. pěst. mat. Vol. 101, 1976, pp. 188-194. · Zbl 0328.46013 [5] Štědrý M.: Periodic solutions of nonlinear equation of a beam with friction. Thesis, 1973. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.