Exact solutions of the generalized Klein–Gordon oscillator in a global monopole space-time

We obtain analytical solutions of the generalized Klein–Gordon relativistic quantum oscillator for spin-zero bosons in the presence of a non-central potential under the influence of a point-like global monopole space-time. The non-central potential consists of r - and θ -dependent potentials S(r, θ ) , and our generalized oscillator involves a function f ( r ), such that the radial part of S(r, θ ) is chosen as the Coulomb and harmonic oscillator potentials, and f ( r ) is selected as the Coulomb and linear functions, respectively. We analyze a θ -dependent potential introduced by Berkdemir. Besides, we find exact analytical solutions of this generalized Klein–Gordon quantum oscillator in such background by means of the Nikiforiov–Uvarov method.