  By the extension of the 3-dimensional analytical solutions of Goldreich and
Weber "P. Goldreich and S. Weber, Homologously Collapsing Stellar Cores,
Astrophys, J. 238, 991 (1980)" with adiabatic exponent gamma=4/3, to the
(classical) Euler-Poisson equations without cosmological constant, the
self-similar (almost re-collapsing) time-periodic solutions with negative
cosmological constant (lambda<0) are constructed. The solutions with
time-periodicity are novel. On basing these solutions, the time-periodic and
almost re-collapsing model is conjectured, for some gaseous stars. Key Words:
Analytically Periodic Solutions, Re-collapsing, Cosmological Constant,
Euler-Poisson Equations, Collapsing
