Nodal Domains for the p-Laplacian
Aomar Anane, Omar Chakrone, Mohamed Filali, Belhadj Karim · 2007
In this paper we consider the eigenvalue problem −pu = λ(m)|u|p−2u, u ∈ W 1,p 0 () where p> 1, p is the p-Laplacian operator, λ> 0, is a bounded domain in RN(N ≥ 1) and m is a given positive function in Lr() (r depending on p and N). We prove that the second positive eigenvalue admits exactly two nodal domains.