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Sign-changing solutions of critical quasilinear Kirchhoff-Schrödinger-Poisson system with logarithmic nonlinearity
AIMS Mathematics 2023, 8(4): 8580-8609
Published: 15 April 2023
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In the present paper, we study the following Kirchhoff-Schrödinger-Poisson system with logarithmic and critical nonlinearity:

{ ( a + b Ω | u | 2 d x ) Δ u + V ( x ) u 1 2 u Δ ( u 2 ) + ϕ u = λ | u | q 2 u ln | u | 2 + | u | 4 u , x Ω , Δ ϕ = u 2 , x Ω , u = ϕ = 0 , x Ω ,

where λ , b > 0 , a > 1 4 , 4 < q < 6 , V ( x ) is a smooth potential function and Ω is a bounded domain in R 3 with Lipschitz boundary. Combining constraint variational method and perturbation method, we prove that the above problem has a least energy sign-changing solution u 0 which has precisely two nodal domains. Moreover, we show that the energy of u 0 is strictly larger than twice the ground state energy.

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