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Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bosegas is studied at finite temperatures in a single-channel mean-field approachwhere the Hartree-Fock energy and pairing gap are determined self-consistently.In the molecular-BEC state, the atomic excitation is gapped and the molecularexcitation is gapless. The binding energy of Feshbach molecules is shifted fromthe vacuum value due to many-body effect. When the scattering length $a_s$ ofatoms is negative, the system is subject to mechanical collapse due to negativecompressibility. The system is stable in most regions with positive scatteringlengths. However at low temperatures near the resonance, the molecular-BECstate vanishes, and the coherent mixture of atomic and molecular BEC is subjectto mechanical collapse.

Molecular Bose-Einstein condensation in a Bose gas with a wide Feshbach resonance at finite temperatures