“…System of equations (10), (13), (14) was analyzed in the Neumann limit, Λ = ∞, of condition (12) for the solid cylinder [37][38][39][40][41][42][43][44] and for studied below geometry of its hollow counterpart [45,46] while the calculations of the combined influence of the magnetic field and real de Gennes distance based on either linear, Eq. (9), [16,17,19,24,[47][48][49][50][51][52][53][54][55] or nonlinear, Eq. (10), [56][57][58][59][60][61][62][63][64] GL theory revealed, for different shapes, a significant influence of the parameter Λ on the nucleation of the superconductivity, critical magnetic fields and localization properties of the superconducting state.…”