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Zbl 1070.34079
Liu, Yansheng; Qi, Aiqin
Positive solutions of nonlinear singular boundary value problem in abstract space. (English)
[J] Comput. Math. Appl. 47, No. 4-5, 683-688 (2004). ISSN 0898-1221

The authors investigate the boundary value problem $$x''(t)+f(t,x(t))=\theta, t\in (0,1),\quad x(0)=x(1)=\theta, \tag P$$ in a Banach space $E$, where $f$ has singularities at $t=0$, $t=1$ and $x=\theta$. \par Under suitable assumptions on $f$, using the Mönch fixed-point theorem, the existence of a positive solution to (P) is proved. An example -- an infinite-dimensional singular differential system, is also presented.
[Rodica Luca (Iaşi)]

MSC 2000:: *34G20 Nonlinear ODE in abstract spaces
34B16 Singular nonlinear boundary value problems
34B18 Positive solutions of nonlinear boundary value problems

Keywords: singular equation; boundary value problem; positive solution; fixed-point; Mönch fixed-point theorem

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