Existence of Julia–Zee dyon and ’t Hooft–Polyakov monopole with new field strength tensor

In this paper, we use a modified Abelian field strength tensor in Georgi–Glashow model and obtain a new Julia–Zee dyon equations which degenerated into the ’t Hooft–Polyakov monopole equations when the profile function J = 0. Combining a three–step iterative shooting argument and a fixed–point theorem approach, we establish the existence of the static solution of the Julia–Zee dyon equations and discuss its qualitative properties. In addition, we show that the total magnetic charge is a constant related to the gauge coupling constant and the total electric charge depend continuously on the profile functions.