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Positive solutions for a beam equation on a nonlinear elastic foundation. (English) Zbl 1060.74035

Summary: We study existence and multiplicity of positive solutions for a fourth-order differential equation with nonlinear boundary conditions modeling beams on elastic foundations. The results are obtained by using variational methods and a maximum principle for fourth-order equations.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74G35 Multiplicity of solutions of equilibrium problems in solid mechanics
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