Yanagida, Eiji; Yotsutani, Shoji Existence of positive radial solutions to \(\Delta u+K(| x| )u^ p=0\) in \(\mathbb R^ n\). (English) Zbl 0813.34036 J. Differ. Equations 115, No. 2, 477-502 (1995). The existence of positive radial solutions to the equation \(\Delta u + K (| x |) u^ P = 0\), \(x \in \mathbb R^ n\), where \(p>1\), \(n>2\), is considered. The following conditions are imposed on \(K(r)\): \(K(r)\) is continuous on \((0, \infty)\); \(K(r) \geq 0\) and \(K(r) \not \equiv 0\) on \((0,\infty)\); \(rK(r) \in L^ 1(0,1)\); \(r^{n - 1 - (n - 2)p} K(r) \in L^ 1(1,\infty)\). Radial solutions are classified as crossing solution, slowly decaying solution and rapidly decaying solution. The main theorem concerns the existence of rapidly decaying solutions and completes results of previous work [N. Kawano and the authors, Funkc. Ekvacioj 36, 557–579 (1993; Zbl 0793.34024)]. Reviewer: P. Drábek (Plzeň) Cited in 1 ReviewCited in 21 Documents MSC: 34C11 Growth and boundedness of solutions to ordinary differential equations 35J60 Nonlinear elliptic equations 35J15 Second-order elliptic equations Keywords:semilinear elliptic problems; positive radial solutions; rapidly decaying solution PDF BibTeX XML Cite \textit{E. Yanagida} and \textit{S. Yotsutani}, J. Differ. Equations 115, No. 2, 477--502 (1995; Zbl 0813.34036) Full Text: DOI