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Zbl 1179.34020
Cid, J.A.; Franco, D.; Minhós, F.
Positive fixed points and fourth-order equations. (English)
[J] Bull. Lond. Math. Soc. 41, No. 1, 72-78 (2009). ISSN 0024-6093; ISSN 1469-2120/e

Consider the boundary value problem $$\aligned u^{(4)} &=\lambda f(t,u,u', u'',u'''),\quad t\in (0,1),\\ u(0) &= u(1)= 0= u''(0)= u''(1).\endaligned\tag{$*$}$$ The authors first improve a fixed point theorem essentially combining the monotone iterative technique with fixed point theorems of cone expansions or compression type. Then they apply it to prove the existence of at least one positive solution of $(*)$ for some open interval of $\lambda$.
[Klaus R. Schneider (Berlin)]

MSC 2000:: *34B18 Positive solutions of nonlinear boundary value problems
34B15 Nonlinear boundary value problems of ODE
34L30 Nonlinear ordinary differential operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34B09 Boundary value problems with an indefinite weight

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