On the Schrödinger–Bopp–Podolsky system: Ground state and least energy nodal solutions with nonsmooth nonlinearity

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In this paper, we investigate a new class of Schrödinger–Bopp–Podolsky systems. Using minimization techniques and the concept of generalized subdifferentials, we establish the existence of a ground state solution with a fixed sign as well as a least energy nodal solution for the system. Furthermore, we demonstrate that the energy of the nodal solution is precisely twice that of the ground state solution.