Local superlinearity for elliptic systems involving parameters

We study the existence, non-existence, and multiplicity of positive solutions for a class of systems of second-order ordinary differential equations using the fixed-point theorem of cone expansion/compression type, the upper-lower solutions method, and degree arguments. We apply our abstract results to study semilinear elliptic systems in bounded annular domains with non-homogeneous boundary conditions. Here the nonlinearities satisfy local superlinear assumptions.