Wu, Jiongqi On positive entire solutions to singular, nonlinear \(p\)-harmonic equations in \(\mathbb{R}^N\, (N\geq 3)\). (Chinese. English summary) Zbl 1056.31005 J. Zhangzhou Teach. Coll., Nat. Sci. 15, No. 1, 1-9 (2002). The \(N\)-dimensional singular nonlinear \(p\)-harmonic equation of the norm \[ \Delta\bigl((\Delta u)^{p-1^*}\bigr)=f\bigl(|x|,u,|\nabla u| \bigr)u^{-\beta},\quad x\in\mathbb{R}^N\quad (N\geq 3) \] is considered, where \(p>1\), \(\beta\geq 0\), \(\xi^{\alpha^*}=|\xi|^{\alpha-1}\xi\), \(\xi\in\mathbb{R}\), \(\alpha >0\), and \(f:\overline\mathbb{R}_+ \times\mathbb{R}_+ \times\overline\mathbb{R}_+\) is a continuous function. The author obtains some sufficient conditions for the existence of infinitely many positive symmetric entire solutions which are bounded or asymptotic to positive constant multiples of \(|x|^{(2p-N)/(p-1)}\) when \(p>N/2\), and \(\log t\) when \(p=N/2\) as \(|x|\to\infty\). Reviewer: Zeng Yuesheng (Huaihua) MSC: 31B30 Biharmonic and polyharmonic equations and functions in higher dimensions 31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions 35J30 Higher-order elliptic equations Keywords:positive symmetric entire solutions PDFBibTeX XMLCite \textit{J. Wu}, J. Zhangzhou Teach. Coll., Nat. Sci. 15, No. 1, 1--9 (2002; Zbl 1056.31005)