  We formulate the GSM in coupled-channel (GSM-CC) representation to describe
low-energy elastic and inelastic scattering of protons on $^{18}$Ne. The GSM-CC
formalism is applied to a translationally-invariant Hamiltonian with an
effective finite-range two-body interaction. We discuss in details the GSM-CC
formalism in coordinate space and give the description of the novel equivalent
potential method for solving the GSM-CC system of integro-differential
equations. We present the first application of the GSM-CC formalism for the
calculation of excited states of $^{18}$Ne and $^{19}$Na, excitation function
and the elastic/inelastic differential cross-sections in the $^{18}$Ne$(p,p')$
reaction at different energies.
