A multiplicity result for critical elliptic problems involving differences of local and nonlocal operators

Publication date: 25 October 2022

Abstract: 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 [20].

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Variational methods for second-order elliptic equations (35J20) Fractional partial differential equations (35R11)

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