Publication Date:
2021-09-15
Description:
In this article, we consider the following quasilinear Schrödinger–Poisson system $$ extstyle egin{cases} -Delta u+V(x)u-uDelta (u^{2})+K(x)phi (x)u=g(x,u), quad xin mathbb{R}^{3}, -Delta phi =K(x)u^{2}, quad xin mathbb{R}^{3}, end{cases} $$ { − Δ u + V ( x ) u − u Δ ( u 2 ) + K ( x ) ϕ ( x ) u = g ( x , u ) , x ∈ R 3 , − Δ ϕ = K ( x ) u 2 , x ∈ R 3 , where $V,K:mathbb{R}^{3}
ightarrow mathbb{R}$ V , K : R 3 → R and $g:mathbb{R}^{3}imes mathbb{R}
ightarrow mathbb{R}$ g : R 3 × R → R are continuous functions; g is of subcritical growth and has some monotonicity properties. The purpose of this paper is to find the ground state solution of (0.1), i.e., a nontrivial solution with the least possible energy by taking advantage of the generalized Nehari manifold approach, which was proposed by Szulkin and Weth. Furthermore, infinitely many geometrically distinct solutions are gained while g is odd in u.
Print ISSN:
1687-2762
Electronic ISSN:
1687-2770
Topics:
Mathematics
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