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Existence results for a model of nonlinear beam on elastic bearings. (English) Zbl 0965.74030
Summary: We study the existence of solutions of the nonlinear fourth-order equation of Kirchhoff type \(u^{(iv)}- m(\int^1_0 |u'(x) |^2 dx)u''+f (x,u)=0\) under nonlinear boundary conditions, which models the deformations of beams on elastic bearings.

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
Full Text: DOI
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