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

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.