journal article
Sep 01, 1988
Eigenoscillations of a string with an additional mass
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References
13
[1]
O. A. Oleinik, “On the eigenoscillations of bodies with concentrated masses,” in: Contemporary Problems of Applied Mathematics and Mathematical Physics [in Russian], Nauka, Moscow (1988).
[2]
O. A. Oleinki, “Homogenization problems in elasticity. Spectra of singularly perturbed operators,” in: Nonclassical Continuum Mechanics, London Math. Soc. Lecture Note Ser., No. 122, Cambridge Univ. Press (1987), pp. 53–95.
10.1017/cbo9780511662911.005
[3]
O. A. Oleinik, “On the frequencies of the eigenoscillations of bodies with concentrated masses,” in: Functional and Numerical Methods of Mathematical Physics [in Russian], Naukova Dumka, Kiev (1988).
[4]
E. Sanchez-Palensia, “Perturbation of eigenvalues in thermoelasticity and vibration of systems with concentrated masses,” in: Trends and Applications of Pure Mathematics to Mechanics, Lecture Notes in Physics, No. 195, Springer, Berlin (1984), pp. 346–368.
10.1007/3-540-12916-2_66
[5]
O. A. Oleinik, “On the spectra of certain singularly perturbed operators,” Usp. Mat. Nauk,42, No. 3, 221–222 (1987).
[6]
A. N. Krylov, “On certain differential equations of mathematical physics, having applications to technical problems,” Izd. Akad. Nauk SSSR, Leningrad (1932), Chap. VII.
[7]
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1972).
[8]
G. A. Iosif'yan, O. A. Oleinik, and A. S. Shamaev, “An asymptotic expansion of the eigenvalues and eigenfunctions of Sturm-Liouville problem with rapidly oscillating coefficients,” Vestn. Mosk. Univ., Ser. I, Mat. Mekh., No. 6, 37–46 (1985).
[9]
I. G. Petrovskii, Lectures on Partial Differential Equations [in Russian], Gos. Izd. Fiz.-Mat. Lit., Moscow (1961).
[10]
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1, Interscience, New York (1966).
[11]
M. I. Vishik and L. A. Lyusternik, “Regular degeneration and boundary layer for linear differential equations with a small parameter,” Usp. Mat. Nauk,12, 3–122 (1957).
[12]
V. G. Maz'ya, S. A. Nazarov, and B. A. Plamenevskii, Asymptotic Behavior of Solutions of Elliptic Boundary Value Problems under Singular Perturbations of the Domain [in Russian], Tbilis. Gos. Univ., Inst. Prikl. Mat., Tbilisi (1981).
[13]
S. A. Nazarov, “The formalism of the construction and the proof of the asymptotic expansions of the solutions of elliptic boundary value problems with a parameter,” Ed. Board of Vestnik Leningrad. Gos. Univ., Moscow (1982) (Manuscript deposited at VINITI, May, 4, 1982, No. 2194-82).
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Details
- Published
- Sep 01, 1988
- Vol/Issue
- 29(5)
- Pages
- 744-760
- License
- View
Cite This Article
Yu. D. Golovatyi, S. A. Nazarov, O. A. Oleinik, et al. (1988). Eigenoscillations of a string with an additional mass. Siberian Mathematical Journal, 29(5), 744-760. https://doi.org/10.1007/bf00970268
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