| Abstract:Since that the accelerated expansion of universe was discovered in 1998, dark energy had became an important part and hot topic in the researching of modern cosmology. Dark energy not only affects the evolvement of the universe, but also affects the equilibrium of stars. Because there is negative pressure caused by dark energy, it is possible to exist the other final state of stars, we named it dark energy stars. A dark energy star model is constructed in this thesis—sine-Gordon soliton star, we found that these soliton stars exist in the form of monster stars .First base on two-dimensional Brans-Dicke gravity model, a soliton star model with the interaction of exotic matter and dark energy is set up by introducing a new metric factor, the numerical calculation gave the distribution graph of density and pressure. The monster star structure was proved according to the solution of the star balance equation, and stability of dark energy in star was also studied. Moreover, the change of matter density and pressure are analyzed by add to the Fermi matter in the weak and strong coupling cases, and the stability of dark energy at finite temperature was discussed.The new works of this thesis are as follows:1. A sine-Gordon soliton star model with exotic matter and dark energy is constructed, the unstable monster structure is found.2. A soliton star with Fermi matter and dark energy is proposed, the stable properties of star are proved. |