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Infinitely Many Solutions for Schrödinger–Poisson Systems and Schrödinger–Kirchhoff Equations

Author

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  • Shibo Liu

    (Department of Mathematics & Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA)

Abstract

By applying Clark’s theorem as altered by Liu and Wang and the truncation method, we obtain a sequence of solutions for a Schrödinger–Poisson system − Δ u + V ( x ) u + ϕ u = f ( u ) in R 3 , − Δ ϕ = u 2 in R 3 with negative energy. A similar result is also obtained for the Schrödinger-Kirchhoff equation as follows: − 1 + ∫ R N ∇ u 2 Δ u + V ( x ) u = f ( u ) u ∈ H 1 ( R N ) .

Suggested Citation

  • Shibo Liu, 2024. "Infinitely Many Solutions for Schrödinger–Poisson Systems and Schrödinger–Kirchhoff Equations," Mathematics, MDPI, vol. 12(14), pages 1-7, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2233-:d:1437328
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