This paper investigates the zero-mass Schrödinger–Poisson equation with a weighted Hardy–Sobolev subcritical exponent: \(\begin{aligned} -\Delta u + \left( \frac{1}{4\pi }|x|^{-1} *u^2\right) u = |x|^b f(u), \quad x \in {\mathbb {R}}^3, \end{aligned}\) where \(-2< b < \infty \) . We develop a novel embedding theorem within the functional space associated with the energy functional of this problem, which differs from previous work (Wang and Su, Appl Math Lett 107:106484, 2020). By employing the symmetric mountain-pass lemma and introducing innovative analytical techniques, we demonstrate that the equation admits infinitely many nontrivial solutions under mild assumptions on the function f. Our findings extend and enhance the results presented in [Ianni and Ruiz, Commun Contemp Math 14(1):1250003, 2012].
