×

zbMATH — the first resource for mathematics

The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation. (English) Zbl 0346.35012

MSC:
35B35 Stability in context of PDEs
35L60 First-order nonlinear hyperbolic equations
35B20 Perturbations in context of PDEs
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] J. Havlová: Periodic solutions of a nonlinear telegraph equation. Čas. pro pěst. matematiky, 90 (1965), pp. 273-289.
[2] A. N. Filatov: Averaging methods in differential and integro-differential equations. FAN, 1971, Taškent · Zbl 0259.34002
[3] J. L. Daleckij M. G. Krejn: The stability of solutions of differential equations in Banach space. Nauka, 1970, Moskva)
[4] J. Kurzweil: Exponentially stable integral manifolds, Averaging principle and the continuous dependence on a parameter. Czech. Math. Journal, 16 (1966), pp. 380-423, 463-492. · Zbl 0186.47603
[5] J. E. Littlewood G. H. Hardy G. Polya: Inequalities. Cambridge University Press, 1934. · JFM 60.0169.01
[6] P. C. Parks: A stability criterion for a panel flutter problem via the second method of Ljapunov. Academic Press Inc., 1967, New York.
[7] J. Pešl: Periodic solutions of a weakly nonlinear wave equation in one dimension. Čas. pro pěst. matematiky, 98 (1974), pp. 333-356.
[8] O. Vejvoda: Periodic solutions of a linear and weakly nonlinear wave equation in one dimension. Czech. Math. Journal, 14 (1964), pp. 341 - 382. · Zbl 0178.45302
[9] O. Vejvoda: The mixed problem and periodic solutions for a linear and weakly nonlinear wave equation in one dimension. Rozpravy ČSAV, Řada mat. a přír. věd, 80 (1970), 3, Academia, Praha. · Zbl 0278.35064
[10] P. K. C. Wang: Stability analysis of elastic and aeroelastic systems via Lyapunov’s direct method. Journal of The Franklin Institute, 1966, Philadelphia. · Zbl 0148.20102
[11] V. I. Zubov: Methods of A. M. Ljapunov and their applications. 1957, Leningrad)
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.