On some third order nonlinear boundary value problems: Existence, location and multiplicity results. (English) Zbl 1144.34009

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 \(s\).


34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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