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Zbl 1099.74030
Drábek, Pavel; Holubová, Gabriela; Matas, Aleš; Nečesal, Petr
Nonlinear models of suspension bridges: discussion of the results.
(English)
[J] Appl. Math., Praha 48, No. 6, 497-514 (2003). ISSN 0862-7940; ISSN 1572-9109/e

Summary: In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by A.\ C.\ Lazer and P.\ J.\ McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.
MSC 2000:
*74H45 Vibrations
34B15 Nonlinear boundary value problems of ODE
35Q72 Other PDE from mechanics
74H60 Dynamical bifurcation
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Keywords: beam equation; system of beam wave equation; initial boundary value problem; bifurcation; Fuč\'{i}k spectrum

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