  In this work, we study low-lying collective excitations of a Bose-Einstein
condensate with Newtonian and Yukawa-like two-particle interaction and derive
boundaries for both Yukawa parameters. Using a variational approach, we
explicitly show for spherical condensate that the corresponding frequencies
depend on the gravitational interaction strength. The acquired results are
presented in contour plots and compared to experimentally verified data from
other tests. Furthermore, we discuss experimental requirements to test our
theoretical model as well as possibilities to improve the boundaries. In
addition, we consider axisymmetric condensates, where it turns out that
disk-shaped BECs lead to better constraints. We also show that in theory we can
determine the values for both Yukawa parameters independently by a measurement
of at least two collective frequencies.
