Existence of least-energy sign-changing solutions for Schrödinger-Poisson system with critical growth

By Da-Bin Wang, Hua-Bo Zhang, Wen Guan. Journal of Mathematical Analysis and Applications, 2019

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Abstract In this paper, we study the following Schrodinger-Poisson system { − Δ u + V ( x ) u + λ ϕ u = | u | 4 u + μ f ( u ) , x ∈ R 3 , − Δ ϕ = u 2 , x ∈ R 3 , where V ( x ) is a smooth function and μ , λ > 0 . Under suitable conditions on f, by using constraint variational method and the quantitative deformation lemma, if μ is large enough, we obtain a least-energy sign-changing (or nodal) solution u λ to this problem for each λ > 0 , and its energy is strictly larger than twice that of the ground state solutions. Moreover, we study the asymptotic behavior of u λ as the parameter λ ↘ 0 .

Subfields: Applied Mathematics, Computational Theory and Mathematics

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