2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95983Static and spherically symmetric perfect fluid solutions of Einstein's field equations with cosmological constant are analysed. After showing existence and uniqueness of a regular solution at the centre the extension of this solution is discussed. Then the existence of global solutions with given equation of state and cosmological constant bounded by 4 pi rho_b, where rho_b is the boundary density (given by the equation of state) of the perfect fluid ball, is proved.13 pages, LaTeX, 1 figure; new reference [7], submitted to the Ukrainian Journal of PhysicsGeneral Relativity and Quantum CosmologyMathematical Physicstext