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  • 1 Central South University, Changsha, Hunan 410083, P. R. China
  • | 2 Central South University, Changsha, Hunan 410083, P. R. China
  • | 3 Central South University, Changsha, Hunan 410083, P. R. China
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This paper is devoted to study the following Schrödinger-Poisson system {Δu+(λa(x)+b(x))u+K(x)ϕu=f(u),x3,Δϕ=4πK(x)u2,x3, where λ is a positive parameter, aC(R3,R+) has a bounded potential well Ω = a−1(0), bC(R3, R) is allowed to be sign-changing, KC(R3, R+) and fC(R, R). Without the monotonicity of f(t)=/|t|3 and the Ambrosetti-Rabinowitz type condition, we establish the existence and exponential decay of positive multi-bump solutions of the above system for λΛ¯, and obtain the concentration of a family of solutions as λ →+∞, where Λ¯>0 is determined by terms of a, b, K and f. Our results improve and generalize the ones obtained by C. O. Alves, M. B. Yang [3] and X. Zhang, S. W. Ma [38].

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