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

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) . [ABSTRACT FROM AUTHOR]