Liouville theorems of integral equations involving the log‐Newtonian potential

Abstract In 1994, Brezis et al. studied the Liouville theorem for the planar Ginzburg–Landau equation, and the result shows that the finite energy solutions have bifurcation properties. In 2001, Hang and Lin generalized this result to the static Landau–Lifschitz type equation. Those equations play an important role in the research of superconducting materials and ferromagnetic materials. The Pohozaev identity is the key tool to the argument there. Recent work has shown that the Pohozaev identity in integral forms can also derive the Liouville theorem for integral equations containing Riesz potentials. In this paper, we also deduce this identity and prove the Liouville theorem under certain conditions, and investigate whether the integrable solutions to the integral equations containing ‐Newtonian potentials have bifurcation properties.