Coupled systems of Hammerstein-type integral equations with sign-changing kernels. (December 2019)

• Record Type: Journal Article
• Authors: de Sousa, Robert; Minhós, Feliz
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 469
• Page End: 483
• Publication Date: 2019-12
• Subjects: Coupled systems -- Hammerstein integral equations -- Sign changing kernels -- Guo–Krasnoselskii theorem -- Arzelà–Ascoli theorem -- Bending of suspension bridges; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this work we consider a generalized coupled systems of two integral equations of Hammerstein-type where the kernel functions may change sign, as well as remain positive on some subintervals, and the nonlinearities may have discontinuities. Moreover the paper provides other new features: The integral equations contain nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation, which increases the range of applications. A new type of cone is introduced, where some requirements may be satisfied only on some subintervals of the domain. Last section contains an application to a coupled system composed by a fourth and second order equations, which models the bending of the main-road of suspension bridges.