Gidas, B.; Spruck, J. Global and local behavior of positive solutions of nonlinear elliptic equations. (English) Zbl 0465.35003 Commun. Pure Appl. Math. 34, 525-598 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 15 ReviewsCited in 623 Documents MSC: 35A20 Analyticity in context of PDEs 35J60 Nonlinear elliptic equations 58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) Keywords:positive solutions; nonlinear elliptic equations; Riemannian manifolds; isolated singularity; results of Liouville type; non-negative Ricci tensor; DeGiorgi-Nash-Moser bootstrap arguments PDF BibTeX XML Cite \textit{B. Gidas} and \textit{J. Spruck}, Commun. Pure Appl. Math. 34, 525--598 (1981; Zbl 0465.35003) Full Text: DOI References: [1] , and , Classification of isolated singularities of nonlinear elliptic equations, to appear. [2] An Introduction to the Study of Stellar Structure, Dover, New York, 1957. [3] Cheng, Comm. Pure Appl. Math. 28 pp 333– (1975) [4] Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations, in Nonlinear Partial Differential Equations in Engineering and Applied Science, Eds. , and , Proc. Conf. Kingston, R.I., 1979, Lect. Notes on Pure Appl. Math. 54, Decker, New York, 1980, pp. 255–273. [5] Gilbarg, J. Analyse Math. 4 pp 309– (1955) [6] and , Elliptic Partial Differential Equations of Second Order, Springer-Verlag, New York, 1977. [7] Joseph, Arch. Rational Mech. Anal. 49 pp 241– (1973) [8] Isolated singularities in semilinear problems, preprint. [9] Littman, Ann. Scuola Norm. Sup. Pisa (3) 17 pp 43– (1963) [10] The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry G, 1971, pp. 247–253. · Zbl 0236.53042 [11] Eigenfunctions of the equation {\(\Delta\)}n + {\(\lambda\)}f(u) = 0, Doklady 165, 1956, pp. 1408–1410. [12] Serrin, Acta Math. 111 pp 247– (1964) [13] Serrin, Acta Math. 113 pp 219– (1965) [14] Serrin, Arch. Rational Math. Anal. 17 pp 67– (1954) [15] Arch. Rational Math. Anal. 20 pp 163– (1965) [16] Trudinger, Comm. Pure Appl. Math. 20 pp 721– (1967) [17] Yau, Comm. Pure Appl. Math. 28 pp 201– (1975) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.