Uniqueness of the positive radial solution on an annulus of the Dirichlet problem for \(\Delta u - u + u^ 3 = 0\)
The author proves uniqueness of the positive radial solution of the Dirichlet problem for \(\Delta u-u+u^3=0\) on the annulus \(\Omega=\{x\in\mathbb{R}^3: R_1<|x|<R_2\}\), where \(0<R_1<R_2\leq+\infty\) and if \(R_2=+\infty\) the Dirichlet condition at \(\infty\) means that the solution belongs to \(L^2(\Omega)\).
scientific article; zbMATH DE number 909997