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On the global solvability of a class of fourth-order nonlinear boundary value problems. (English) Zbl 0913.34020
Summary: This paper is concerned with the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of an elastic beam which is acted upon by axial compression, lateral forces and is in contact with a semi-infinite medium acting as a foundation. For certain ranges of the acting axial compression force, the solvability of the equations follows from the coercivity of their linear parts. Beyond these ranges this coercivity is lost. It is shown that the coercivity which ensures the global solvability can be generated by the nonlinear parts of the equations for a certain type of foundation.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
74K15 Membranes
74G60 Bifurcation and buckling
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