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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Xiaoli Lu,
  • Jing Zhang

摘要

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.