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Existence results and numerical solutions for a beam equation with nonlinear boundary conditions. (English) Zbl 1068.74038
Summary: We study the existence of solutions of the nonlinear fourth-order equation of Kirchhoff type \[ u^{(iv)}- m\Biggl(\int^L_0|u'(s)|^2 ds\Biggr) u''= f(x, u), \] under nonlinear boundary conditions which models the deformations of beams on elastic supports.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G20 Local existence of solutions (near a given solution) for equilibrium problems in solid mechanics (MSC2010)
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