Normalized solutions to the p -Laplacian Schrödinger–Poisson system with mass supercritical growth
Kai Liu, Xiaoming He · Bulletin of Mathematical Sciences · 2025
In this paper, we address the existence and qualitative features of ground states associated with the p-Laplacian Schrödinger–Poisson system: [Formula: see text] under the mass constraint [Formula: see text] The nonlinearity f is assumed to be mass super-critical, while the parameter satisfies [Formula: see text]. In the case [Formula: see text] and [Formula: see text], we establish the existence of ground states as well as infinitely many radially symmetric solutions. The proof is based on constructing an appropriate bounded Palais–Smale sequence combined with genus theory. Moreover, by employing the Pohozaev manifold framework, we derive a nonexistence result in the regime [Formula: see text] and [Formula: see text]. In contrast, for the case [Formula: see text] with [Formula: see text], variational methods enable us to prove the existence of solutions.