Positive solutions of nonlinear beam equations with time and space singularities (Q607330)

Existence and multiplicity of positive solutions of a nonlinear fourth-order ordinary differential equation under linear two-point boundary conditions is proved under appropriate conditions on the nonlinear term \(f=f(t,u,u')\), which may be singular on time and/or space. The case in which the nonlinearity \(f\) does not depend on \(u'\) is treated separately. Height functions are introduced in order to set convenient conditions that allow the use of the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type.