Existence of U(1) gauged Q-balls for a field model with sixth-order potential

Q-balls are non-topological solitons in a large family of field theories. We focus on the existence of U(1) gauged Q-balls for a field theory with sixth-order potential. The problem can be reduced to proving the existence of critical points for some indefinite functional. For this, we use a constrained minimization approach to obtain the existence of critical points. Moreover, we establish some qualitative properties of the Q-ball solution, such as monotonicity, boundedness and asymptotic behavior.