On some third order nonlinear boundary value problems: Existence, location and multiplicity results (Q2465890)

An Ambrosetti-Prodi type result is proved for the semilinear third order equation \[ u'''(t) + f(t,u(t),u'(t),u''(t)) = s\,p(t) \] under different two-point linear boundary conditions. Upper and lower solutions techniques and topological degree theory are used. A Nagumo condition is used in order to obtain a priori bounds for the second derivative. Existence, nonexistence and multiplicity of solutions is discussed for different ranges of the parameter \(s\).