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September 10, 2025Open Access

Existence of local minimizers for a critical problem involving a superposition operator of mixed fractional order

Key Points

Local minimizers exist for a critical problem involving mixed fractional order superposition operators.
The main finding indicates that local minimizers can be established under specific conditions.
This investigation extends earlier results related to Riemannian manifolds to a new framework.
The implications of this work may enhance understanding in the analysis of mixed fractional operators.

Abstract

We prove the existence of local minimizers for a critical problem involving a superposition operator of mixed fractional order recently introduced in S. Dipierro, K. Perera, C. Sportelli and E. Valdinoci, An existence theory for superposition operators of mixed order subject to jumping nonlinearities, Nonlinearity 37(5) (2024) 055018. Our approach extends a result from G. M. Bisci, D. Repovš and L. Vilasi, Existence results for some problems on Riemannian manifolds, Commun. Anal. Geom. 28(3) (2020) 677–706 to this framework.

Existence of local minimizers for a critical problem involving a superposition operator of mixed fractional order

Key Points

Abstract

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