Mixed symmetry superconductivity in two-dimensional Fermi liquids

We consider a 2D isotropic Fermi liquid with attraction in both $s$ and $d$ channels and examine the possibility of a superconducting state with mixed $s$ and $d$ symmetry of the gap function. We show that both in the weak coupling limit and at strong coupling, a mixed $s+id$ symmetry state is realized in a certain range of interaction. Phase transitions between the mixed and the pure symmetry states are second order. We also show that there is no stable mixed $s+d$ symmetry state at any coupling.