This investigation demonstrates the existence of ground state solutions using variational and analytical techniques, indicating novel implications for mathematical physics.
In this article, we investigate the existence of ground state solutions for the following generalized Schrödinger–Poisson system: { − Δ u + u + κ ϕ g ( u ) = f ( u ) , in R 3 , − Δ ϕ = G ( u ) , in R 3 , where κ > 0 is a parameter, g = G ′ ∈ C ( R , R ) , and f ∈ C ( R , R ) . By combining the monotonicity trick with refined variational and analytical techniques, we establish the existence of ground state solutions for the above system under mild assumptions on f and g .
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Yang et al. (2025) studied this question.
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