Citti, Giovanna Positive solutions for a quasilinear degenerate elliptic equation in \(\mathbb R^ N\). (English) Zbl 0659.35039 Rend. Circ. Mat. Palermo, II. Ser. 35, 364-375 (1986). The existence of a positive, spherically symmetric solution on \(\mathbb R^ N\), which vanishes as \(| x| \to +\infty\), of the degenerate elliptic equation \(D(| Du|^{p-2} Du)+f(u)=0\) is studied. The method used in the proof of the existence of such a solution is the constrained minimization method as by H. Berestycki and P. L. Lions [Arch. Ration. Mech. Anal. 82, 313–345 (1983; Zbl 0533.35029)] for the linear case \((p=2)\). Reviewer: Marco Biroli (Milano) Cited in 1 ReviewCited in 15 Documents MSC: 35J62 Quasilinear elliptic equations 35J70 Degenerate elliptic equations 35D30 Weak solutions to PDEs 35B09 Positive solutions to PDEs Keywords:existence; positive; spherically symmetric; constrained minimization method Citations:Zbl 0533.35029 PDFBibTeX XMLCite \textit{G. Citti}, Rend. Circ. Mat. Palermo (2) 35, 364--375 (1986; Zbl 0659.35039) Full Text: DOI References: [1] Berestycki H., Lions P.L.,Nonlinear scalar field equations, I, Arch. Rat. Mech. and Anal.,82 (1983), 313–345. · Zbl 0533.35029 [2] Coleman S., Glazer V., Martin A.,Action minima among solutions to a class of Euclidean scalar field equations, Comm. Math., Phys.,58 (1978), 211–221. · doi:10.1007/BF01609421 [3] Ni W.M., Serrin J.,Non-existence theorems for quasilinear partial differential equations, To appear, Rend. Circolo Mat. Palermo,5 (1985). · Zbl 0625.35028 [4] Strauss W.A.,Existence of solitary waves in higher dimensions, Comm. Math. Phys.,55 (1977), 149–162. · Zbl 0356.35028 · doi:10.1007/BF01626517 [5] Talenti G.,Best constant in Sobolev inequality, Ann. Mat. Pura ed Appl.,110 (1976), 353–372. · Zbl 0353.46018 · doi:10.1007/BF02418013 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.