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Herrmann, Leopold

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

Czech. Math. J. 30(105), 177-206 (1980).
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Cited in 5 Documents

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

Keywords:

periodic solutions of abstract and partial differential equations; Fourier method; regularity of solutions; energy; regularization procedure; weakly nonlinear problems; second order elliptic operator
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\textit{L. Herrmann}, Czech. Math. J. 30(105), 177--206 (1980; Zbl 0445.35013)
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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
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.