×

Periodic solutions of the equation \(u_{tt}+u_{xxxx}=\varepsilon f(.,.,u,u_t)\). (English) Zbl 0263.35017


MSC:

35G20 Nonlinear higher-order PDEs
35B10 Periodic solutions to PDEs
35B20 Perturbations in context of PDEs
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] Hall W. S.: On the existence of periodic solutions for the equations \(D_{tt}u+(-1)^{p}\,D_{x}^{2p}u=\varepsilon f(\cdot ,\cdot ,u)\). Jour. of Diff. Equations, 7, 509-526, 1970. · Zbl 0198.14002
[2] Hall W. S.: Periodic solutions of a class of weakly nonlinear evolution equations. Arch. Rat. Mech. Anal., Vol. 39, 4, 294-322. · Zbl 0211.12704
[3] Lovicarová H.: Periodic solutions of a weakly nonlinear wave equation in one dimension. Czech. Math. J. 19, 1969, 324-342. · Zbl 0181.10901
[4] Krylová N.: Periodic solutions of hyperbolic partial differential equation with quadratic dissipative term. Czech. Math. J. 20, 1970, 375-405. · Zbl 0214.10402
[5] Krylová N., Vejvoda O.: A linear and weakly nonlinear equation of a beam: The boundary-value problem for free extremities and its periodic solutions. Czech. Math. J. 21, 1971, 535-566. · Zbl 0226.35008
[6] Moser J.: A rapidly convergent iteration method and nonlinear partial differential equations. Ann. Scuola Norm. Super. Pisa, Ser. 3, 20, 1956, 265-315. · Zbl 0144.18202
[7] Rabinowitz P. H.: Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure Appl. Math., 20, 1967, 145-205. · Zbl 0152.10003
[8] Rabinowitz P. H.: Time periodic solutions of nonlinear wave equations. Manuscripta math., 5, 1971, 165-194. · Zbl 0219.35062
[9] De Simon L., Torelli C.: Soluzioni periodiche di equazioni a derivate parziali di tipo iperbolico non lineari. Rend. Sem. Mat. Univ. Padova XL, 1968, 380-401. · Zbl 0198.13704
[10] Torelli G.: Soluzioni periodiche dell’equazione non lineare \(u_{tt}-u_{xx} + f(x, t, u) = 0\). Rend. Ist. di Matem. Univ. Trieste 1, 1969, 123-137. · Zbl 0186.42903
[11] Petryshyn W. V.: On nonlinear \(P\)-compact operators in Banach space with applications to constructive fixed-point theorems. J. Math. Anal. Appl. 15, 1966, 228-242. · Zbl 0149.10602
[12] Bers L., John F., Schechter W.: Partial Differential Equations. New York, Interscience 1964. · Zbl 0126.00207
[13] Randol B.: A lattice-point problem II. TAMS 125, 1966, 101-113. · Zbl 0161.04902
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.