Xu, Xingye The positive entire solutions for a class of nonlinear biharmonic equations with singularity on \(\mathbb R^n\). (Chinese. English summary) Zbl 1199.35074 Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 87-93 (2009). Summary: The author’s aim is to establish theorems of existence of positive radially symmetric entire solutions for a class of singular nonlinear biharmonic equation \(\Delta^2 u=f(|x|, u, |\nabla u|)u^{-\beta}\) (\(x\in \mathbb R^n\), \(n\geq 3\), \(\beta>0\)) on \(\mathbb R^n\) with the Schauder-Tikhonov fixed point theorem as the principal tool, and it presents the properties of the solutions. MSC: 35J40 Boundary value problems for higher-order elliptic equations 35J75 Singular elliptic equations 35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian 47N20 Applications of operator theory to differential and integral equations Keywords:biharmonic equation; positive entire solution; Lebesgue dominated convergence theorem; equicontinuity; fixed point theorem PDFBibTeX XMLCite \textit{X. Xu}, Acta Math. Sci., Ser. A, Chin. Ed. 29, No. 1, 87--93 (2009; Zbl 1199.35074)