Abstract

本文研究Schrodinger-Poisson-Slater (SPS) 方程 i∂ ψ /∂ t +△ ψ -χ(| x | -1 *| ψ | 2 ) ψ + | ψ | p-1 ψ = 0, χ > 0, x ∈ R 3 , 当 p > 7/3 时, 运用变分法证明SPS 方程的基态驻波强不稳定, 并进一步用基态驻波解刻画SPS 方程 的解在有限时间爆破的门槛初始条件; 在 p = 7/3 时, 建立了基态驻波解的 L 2 范数的下界.

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