Nonzero radial solutions for elliptic systems with coupled functional   BCs in exterior domains
  We prove new results on the existence, non-existence, localization and multiplicity of nontrivial radial solutions of a system of elliptic boundary value problems on exterior domains subject to nonlocal, nonlinear, functional boundary conditions. Our approach relies on fixed point index theory. As a by-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 explicit nonlinearities in order to illustrate our theory. 
Filomena Cianciaruso, Gennaro Infante and Paolamaria Pietramala
math.AP math.CA