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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.

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