Existence results for nonhomogeneous quasilinear critical Kirchhoff–Schrödinger–Poisson system

We study the quasilinear Kirchhoff–Schrödinger–Poisson system with logarithmic and critical nonlinearity. Under certain assumptions, we discuss the existence of solutions in two different situations. Firstly, in the homogeneous case, we prove the existence of nontrivial nonnegative and nonpositive solutions, a sequence of high-energy solutions via the perturbation method. Later, in the nonhomogeneous case, we prove that the system admits at least two solutions with different energies by using Ekeland’s variational principle and the mountain pass theorem.