Coclite, M. M.; Palmieri, G. On a singular nonlinear Dirichlet problem. (English) Zbl 0692.35047 Commun. Partial Differ. Equations 14, No. 10, 1315-1327 (1989). The authors are studying the existence of positive solutions of the semilinear equation \(\Delta u+g(x,u)+h(x,\lambda u)=0,\) with zero boundary data, in a boundary smooth domain in \({\mathbb{R}}^ n\). Here, \(\lambda\) is a positive bifurcation parameter. It is assumed that the functions g(x,u) and h(x,\(\lambda\) u) satisfy some conditions so that they resemble the behaviour of \(u^{-\alpha}\), \(\alpha >0\) and \((\lambda u)^ p\), \(p>0\) respectively. The authors proves existence/nonexistence results depending on the parameter \(\lambda\). The use upper and lower solution techniques. Reviewer: H.Egnell Cited in 4 ReviewsCited in 158 Documents MSC: 35J65 Nonlinear boundary value problems for linear elliptic equations 35B32 Bifurcations in context of PDEs 35J70 Degenerate elliptic equations Keywords:positive solutions; semilinear equation; bifurcation parameter; existence/nonexistence results; upper and lower solution PDFBibTeX XMLCite \textit{M. M. Coclite} and \textit{G. Palmieri}, Commun. Partial Differ. Equations 14, No. 10, 1315--1327 (1989; Zbl 0692.35047) Full Text: DOI References: [1] Adamas, R.A. 1975. ”Sobolev Spaces”. New York-San Francisco - London: Academic Press. [2] Agmon S, Ann. Sc. Norm. Sup. Pisa pp 405– (1959) [3] DOI: 10.1512/iumj.1971.21.21012 [4] DOI: 10.1080/03605307708820029 · Zbl 0362.35031 [5] Fulks W., Osaka Math J. 12 pp 1– (1960) [6] DOI: 10.1137/0517096 · Zbl 0614.35037 [7] Keller H. B., J. Math. Mech. 16 pp 1361– (1967) [8] Ladyzenskaja, O.A. 1968. ”Equations aux dérivées partielles de type elliptique”. Paris: Dunod. [9] DOI: 10.1007/BF01214274 · Zbl 0324.35037 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.