A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators
Kanishka Perera, Caterina Sportelli · Topological Methods in Nonlinear Analysis · 2024
We study some critical elliptic problems involving the difference of two nonlocal operators, or the difference of a local operator and a nonlocal operator. The main result is the existence of two nontrivial weak solutions, one with negative energy and the other with positive energy, for all sufficiently small values of a parameter. The proof is based on an abstract result recently obtained in \cite{MR4293883}.