Periodic solutions of a piecewise linear beam equation damping and nonconstant load.
Periodic solutions of nonlinear vibrating beams.
Periodic vibrations of an extensible beam
Periodically forced damped beams resting on nonlinear elastic bearings
Positive solutions for some beam equation boundary value problems.
Positive solutions to a class of elastic beam equations with semipositone nonlinearity
Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem , 0 < t < 1, u(0) = u’(0) = u’(1) =u”’(1) =0, where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the deflection of...