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The positive entire solutions for a class of nonlinear biharmonic equations with singularity on \(\mathbb R^n\). (Chinese. English summary) Zbl 1199.35074

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
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