| Summary: | 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.
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