Wave breaking criteria for a generalized Dullin<inline-formula><tex-math id="M1">$ - $</tex-math></inline-formula>Gottwald<inline-formula><tex-math id="M2">$ - $</tex-math></inline-formula>Holm equation with weak dissipation

A generalized Dullin-Gottwald-Holm equation with weak dissipation is investigated. Employing the approaches relating the Lyapunov functions, we establish the wave breaking criteria of non-periodic solutions for the equation in the situation that is not considered in Cheng and Li [Appl Math Lett (2025,163: 109455)].