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We prove new results on the existence, non-existence, localization andmultiplicity of nontrivial radial solutions of a system of elliptic boundaryvalue problems on exterior domains subject to nonlocal, nonlinear, functionalboundary conditions. Our approach relies on fixed point index theory. As aby-product of our theory we provide an answer to an open question posed by do{\'O}, Lorca, S\'{a}nchez and Ubilla. We include some examples with explicitnonlinearities in order to illustrate our theory.

Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains