  We consider the nonexistence of minimizers for the energy containing a
nonlocal perimeter with a general kernel $K$, a Riesz potential, and a
background potential in $\mathbb{R}^N$ with $N\geq2$ under the volume
constraint. We show that the energy has no minimizer for a sufficiently large
mass under suitable assumptions on $K$. The proof is based on the partition of
a minimizer and the comparison of the sum of the energy for each part with the
energy for the original configuration. This strategy is shown in [R.A. Frank,
R. Killip, P.T. Nam, 2016] and [D.A. La Manna, 2018]
