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Application of Moser’s method to a certain type of evolution equations. (English) Zbl 0547.35081
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

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
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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
[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.
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