2024/10/17 by Serena Dipierro, Kanishka Perera, Caterina Sportelli +1 · 15 citations
Mathematics · #Applied mathematics #Approximation Theory and Sequence Spaces #Fractional Differential Equations Solutions #Mathematical analysis #Mathematics #Nonlinear Differential Equations Analysis #Nonlinear system #Order (exchange) #Pure mathematics #Superposition principle
paper · doi:10.1142/s0219199725500051
published in Communications in Contemporary Mathematics 27(08) (World Scientific)
openalex publication_date 2024/10/17 · crossref created 2024/10/17 · crossref issued 2024/12/14 · crossref published 2024/12/14 · crossref published-online 2024/12/14 · crossref deposited 2025/07/29 · crossref published-print 2025/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01 · crossref indexed 2026/08/06
We establish the existence of multiple solutions for a nonlinear problem of critical type. The problem considered is fractional in nature, since it is obtained by the superposition of [Formula: see text]-fractional Laplacians of different orders. The results obtained are new even in the case of the sum of two different fractional [Formula: see text]-Laplacians, or the sum of a fractional [Formula: see text]-Laplacian and a classical [Formula: see text]-Laplacian, but our framework is general enough to address also the sum of finitely, or even infinitely many, operators. In fact, we can also consider the superposition of a continuum of operators, modulated by a general signed measure on the fractional exponents. When this measure is not positive, the contributions of the individual operators to the whole superposition operator is allowed to change sign. In this situation, our structural assumption is that the positive measure on the higher fractional exponents dominates the rest of the signed measure.