×

On the existence of positive solutions of a singular nonlinear differential equation. (English) Zbl 1007.34079

From the authors’ abstract: We consider the nonlinear singular differential equation \(A^{-1}(Au')'- \mu u= -\sigma f(\cdot,u)\) on \((0,\omega)\), \(\omega\in (0,\infty]\), where \(\mu\) and \(\sigma\) are two positive Radon measures on \((0,\omega)\) not charging points. For a regular function \(f\) and under some hypotheses on \(A\), we prove the existence of an infinite number of nonnegative solutions.

MSC:

34L30 Nonlinear ordinary differential operators
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Dalmasso, R., On singular nonlinear elliptic problems of second and fourth orders, Bull. Soc. Math., 116, 95-110 (1992) · Zbl 0809.35024
[2] Maâgli, H.; Masmoudi, S., Sur les solutions d’un opérateur différentiel singulier semi-linéaire, Potential Anal., 10, 289-304 (1999) · Zbl 0935.34011
[3] Usami, H., On a singular elliptic boundary value problem in a ball, Nonlinear Anal., 13, 1163-1170 (1989) · Zbl 0707.35058
[4] 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.