Ground state solution for the Choquard equation under the superposition of operators of mixed fractional order

We establish the existence of a ground state solution for the fractional Choquard equation governed by the superposition operator ∫ [0, 1] (- )ˢ u\, dμ (s), ∫ [ 0 , 1 ] ( - Δ ) s u d μ ( s ) , and in presence of a confining potential. Here, μ μ denotes a signed measure on the interval of fractional exponents [0, 1]. The presence of the superposition operator asks for the problem to be addressed with a special care. However, the wide generality of this setting allows to provide entirely new existence results in several special cases of interest, including, e.g., the mixed operator one - + (- )ˢ - Δ + ( - Δ ) s . We point out that the possibility of considering operators “with the wrong sign" is also a complete novelty.