This paper surveys an area of nonlinear functional analysis and its applications. The main application is to the existence and multiplicity of periodic solutions of a possible mathematical models of nonlinearly supported bending beams, and their possible application to nonlinear behavior as observed in large-amplitude flexings in suspension bridges. A second area, periodic flexings in a floating beam, also nonlinearly supported, is covered a t the end of the paper.

Abstract.We consider the singular boundary-value problem Au+p(x)u~7 = 0 in d, u | 9Í2 = 0 , where y > 0 . Under the assumption p(x) > 0 and certain smoothness assumptions, we show that there exists a solution which is smooth on £2 and continuous on Í2 .

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