The further analytical discussions on the U(1) gauged Q-balls with N-power potential

We pay our analytical discussions on the $U(1)$ gauged Q-balls with $N$-power potential to examine their properties although more numerical descriptions and some analytical consideration have been contributed to those governed by four-power potential. We also demonstrate strictly some new limitations that the stable $U(1)$ gauged Q-balls should accept instead of estimating those with only some specific values of model variables numerically. According to the explicit expressions of radius, the Noether charge and energy of the gauged Q-balls from our burden derivation, it is found analytically that these models under the potential of matter field with general power and the boundary conditions that the fields must obey will exist instead of dispersing and decaying while the Noether charge of the large gauged Q-balls is limited. The mass parameter of the model can not be tiny.