Existence and localization of solutions for operatorial systems defined on Cartesian product of Fréchet spaces using a new vector version of Krasnoselskii's cone compression-expansion theorem

A generalization of Krasnoselskii's compression-expansion fixed point theorem is presented for treating nonlinear systems defined on the Cartesian product of Fréchet spaces. The compression-expansion conditions are given componentwise, and therefore each component can separately behave in its own way. Applications to differential systems of second order on the half line are presented, with existence, localization and multiplicity results.