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Zbl 0979.34015
De Coster, C.; Sanchez, L.
Upper and lower solutions, Ambrosetti-Prodi problem and positive solutions for fourth order O. D. E.
(English)
[J] Riv. Mat. Pura Appl. 14, 57-82 (1994). ISSN 1121-7111

Summary: The authors study the method of upper and lower solutions for the fourth-order equation $u^{(4)}= f(t,u)$ with the boundary conditions $u(0)= 0= u(\pi)$, $u''(0)= 0= u''(\pi)$. This is used to derive results for the corresponding Ambrosetti-Prodi problem. Also, the multiplicity of positive solutions is studied in the case of oscillating'' nonlinearity. Variational methods are used throughout.
MSC 2000:
*34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE

Keywords: Ambrosetti-Prodi problem; positive solutions

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