Entire solutions and global bifurcations for a biharmonic equation with singular non-linearity in \(\mathbb{R}^3\)
The first part of the paper is devoted to studying existence, uniqueness and asymptotic behaviour of radial solutions of the biharmonic equation \( - \Delta ^{2} u = u ^{-2}\) in \( {\mathbb R}^{2} \) and \( {\mathbb R}^{3} \). Applications are given, in the second part of the paper, to studying the structure of solutions of the boundary value problem \( \Delta ^{2}u= \lambda /(1 - u ) ^{2}\), \(u= \Delta u=0\) on \( \partial B\) where \(B\) is the unit ball in \( {\mathbb R}^{3} \).
scientific article; zbMATH DE number 5572594
scientific article