Maatoug, L.; Zribi, M. On the existence of positive solutions of nonlinear differential equations of high order. (English) Zbl 0990.34025 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 43, No. 6, 721-731 (2001). Here, the authors prove, that the infinitely many solutions result by Zhao is applicable to the following nonlinear differential equation \[ L^2= L(Lu)= -f(.,u)\quad\text{in }(0,\omega), \] with \(\omega\in (0,\infty]\), \(f\) a measurable function on \((0,\omega)\times (0,\infty)\) dominated by a regular function, and \(L\) the differential operator of second order defined on \((0,\omega)\) by \(Lu={1\over A} (Au')'\), where \(A\) is a continuous function on \([0,\omega)\), infinitely differentiable and positive on \((0,\omega)\). Reviewer: Dara Moazzami (Tehran) MSC: 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B16 Singular nonlinear boundary value problems for ordinary differential equations Keywords:nonlinear; singular; positive solution; Green’s function; fixed-point; existence PDFBibTeX XMLCite \textit{L. Maatoug} and \textit{M. Zribi}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 43, No. 6, 721--731 (2001; Zbl 0990.34025) Full Text: DOI References: [1] Dalmasso, R., On singular nonlinear elliptic problems of second and fourth orders, Bull. Sci. Math., 116, 2, 95-110 (1992) · Zbl 0809.35024 [2] H. Maâgli, S. Masmoudi, Sur les solutions d’un opérateur différentiel singulier semi-linéaire, Potential Analysis, to appear.; H. Maâgli, S. Masmoudi, Sur les solutions d’un opérateur différentiel singulier semi-linéaire, Potential Analysis, to appear. [3] Zhao, Z., Positive solutions of nonlinear second order ordinary differential equations, Proc. Amer. Math. Soc., 121, 465-469 (1994) · Zbl 0802.34026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.