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

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

Mathematics, 2024, vol. 12, issue 14, 1-7

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 ) .

Keywords: Schrödinger equations; Clark’s theorem; truncation method; Palais–Smale condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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