Nonzero positive solutions of fractional Laplacian systems with functional terms. Issue 1 (14th December 2022)

• Record Type: Journal Article
• Authors: Biagi, Stefano; Calamai, Alessandro; Infante, Gennaro
• Is Part Of: Mathematische Nachrichten. Volume 296:Issue 1(2023)
• Page Start: 102
• Page End: 121
• Publication Date: 2022-12-14
• Subjects: cone -- fixed point index -- fractional Laplacian -- functional boundary condition -- nonlocal functional weights -- positive solution; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.202100074
• Languages: English
• ISSNs: 0025-584X

Abstract

Abstract: We study the existence of nonzero positive solutions of a class of systems of differential equations driven by fractional powers of the Laplacian. Our approach is based on the notion of fixed point index, and allows us to deal with nonlocal functional weights and functional boundary conditions. We present two examples to shed light on the type of functionals and growth conditions that can be considered with our approach.