The following Dirichlet problem is considered, where Ω is either an annulus or a ball in RN and p > 1. The uniqueness of radial solutions having exactly k-1 nodes is shown for the following cases: Ω is a sufficiently thin annulus; Ω is a certain small ball, N ≥ 4 and 1 < p < N/(N-2); Ω is the unit ball, N =3 and 1 < p ≤ 3; Ω is any annulus or any ball, but p >1 is sufficiently close to 1 and N = 3, 5 or 7.
- Modified Bessel functions
- Scalar field equation
- Sign-changing radial solutions
ASJC Scopus subject areas
- Applied Mathematics