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Zbl 1125.34010
Cabada, Alberto; Cid, J.Ángel; Sanchez, Lu{\'\i}s
Positivity and lower and upper solutions for fourth order boundary value problems.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 67, No. 5, A, 1599-1612 (2007). ISSN 0362-546X

The authors are concerned with existence and multiplicity of solutions of the fourth order boundary value problem $$u^{(4)}=f(t,u(t)),\quad t\in [0,1], \quad u(0)=u(1)=u''(0)=u''(1)=0$$ in the presence of a pair of, not necessarily ordered, lower and upper solutions. The proof of the main results are based upon maximum principles and Amann's three solutions theorem [see {\it H. Amann}, J. Funct. Anal. 11, 346--384 (1972; Zbl 0244.47046)].
[Ruyun Ma (Lanzhou)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
34B27 Green functions

Keywords: upper and lower solutions; fourth order maximum principles; multiple solutions

Citations: Zbl 0244.47046

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