Work

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

Year: 2026

Type: article

Abstract: We establish the existence of a ground state solution for the fractional Choquard equation governed by the superposition operator $$ \int _{[0, 1]} (-\varDelta )^s u\, d\mu (s), $$ ∫ [ 0 , 1 ] ( - Δ ) s u d μ ( s ) , and in presence of a confining potential. Here, $$\mu $$ 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 $$-\varDelta + (-\varDelta )^s$$ - Δ + ( - Δ ) s . We point out that the possibility of considering operators “with the wrong sign" is also a complete novelty.

Source: Fractional Calculus and Applied Analysis

DOI: 10.1007/s13540-026-00512-x

Authors: Edoardo Proietti Lippi, Caterina Sportelli

Institutions: The University of Western Australia, Universidad de Granada

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,590