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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 \(s\).

MSC:

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

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