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Periodic solutions of abstract differential equations: the Fourier method. (English) Zbl 0445.35013


MSC:

35B10 Periodic solutions to PDEs
35J15 Second-order elliptic equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35C10 Series solutions to PDEs
35K10 Second-order parabolic equations
35L10 Second-order hyperbolic equations
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References:

[1] S. Agmon: Lectures on elliptic boundary value problems. Van Nostrand, Princeton-New Jersey 1965. · Zbl 0142.37401
[2] O. V. Běsov V. P. Iljin S. M. Nikol’skij: Integral representations of functions and embedding theorems. (Russian.) Izd. Nauka, Moskva 1975.
[3] A. I. Hinčin: Continued fractions. (Russian.) Fizmatgiz, Moskva 1961.
[4] A. Kufner J. Kadlec: Fourier series. Academia, Praha 1971. · Zbl 0215.17901
[5] O. A. Ladyženskaja: Mixed problem for a hyperbolic equation. (Russian.) Gos. izd. teh.-teor. lit., Moskva 1953.
[6] J.-L. Lions: Equations différentielles opérationnelles et problèmes aux limites. Springer-Verlag, Berlin-Göttingen-Heidelberg 1961. · Zbl 0098.31101
[7] J.-L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris 1969. · Zbl 0189.40603
[8] J.-L. Lions E. Magenes: Problèmes aux limites non homogenes et applications I. Dunod, Paris 1968. · Zbl 0165.10801
[9] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha 1967. · Zbl 1225.35003
[10] B. Novák: Remark on periodic solutions of linear wave equation in one dimension. Comment. Math. Univ. Carolinae 15 (1974), 513 - 519.
[11] G. Prodi A. Ambrosetti: Analisi nonlineare. Scuola normale superiore. Pisa 1973. · Zbl 0352.47001
[12] P. H. Rabinowitz: Periodic solutions of nonlinear hyperbolic partial differential equations. Comm. Pure Appl. Math. 20 (1967), 145-205. · Zbl 0152.10003
[13] I. Straškraba: Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces. Czechoslovak Math. J. · Zbl 0893.35100
[14] H. Triebel: Höhere Analysis. VEB, Berlin 1972. · Zbl 0257.47001
[15] O. Vejvoda, al.: Partial differential equations: time periodic solutions. Sijthoff-Nordhoff · Zbl 0501.35001
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