A divergence-type identity in a punctured domain and its application to a singular polyharmonic problem
In the present study the authors deal with the solutions of \[ (-\Delta)^pu= f(x,u)\quad\text{in}\,\Omega\setminus\{0\},\;n> 2p,\tag{1} \] where \(\Omega= \mathbb R^n\) or \(\mathbb B_1(0)\) and \(f(x,t)\) satisfies that there exists \(s_0\geq 0\) and \(t_0\geq 0\) such that \(f(x,t)\geq c|x|^{-\sigma} t^q\) for \(0<|x|< s_0\) and \(t\geq t_0\) with some \(\sigma\geq n-q(n- 2p)\) and \(q> 1\). The authors show that a divergence-type identity is valid for positive solutions of (1).
scientific article; zbMATH DE number 2145904