arXiv:2210.14230 Abstract | arXiv Analytics

arXiv:2210.14230 [math.AP]Abstract References Reviews Resources

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

Published 2022-10-25Version 1

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].

Comments: Preprint. arXiv admin note: substantial text overlap with arXiv:2210.13742, arXiv:2102.09131

Categories: math.AP

Subjects: 35R11, 35B33, 35J20

Keywords: critical elliptic problems, nonlocal operator, multiplicity result, difference, nontrivial weak solutions

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