Uniqueness for positive solutions of \(p\)-Laplacian problem in an annulus
In an annulus the \(p\)-Laplacian with homogeneous Dirichlet boundary conditions is studied on the uniqueness of positive radial solutions. First using change of variables the problem is reformulated into an equivalent Dirichlet problem for an ordinary differential equation (ODE). Then a suitable initial value problem for this ODE is studied in detail. Using these results and a shooting method the uniqueness of the solution of a homogeneous Dirichlet problem for the ODE is proved. The equivalence between the ODE and the \(p\)-Laplacian under consideration gives the uniqueness result for the original problem.
scientific article; zbMATH DE number 1491218