具有线性约束非线性的准线性薛定谔-泊松系统的解

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引用次数: 0

摘要

Abstract In this paper, we are concerned with following quasilinear Schrödinger-Poisson system $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+ K(x)\phi u=f(x,u),\quad &;{}x\in {\mathbb {R}}^3,\ -\Delta \phi -\varepsilon ^4\Delta _4\phi = K(x) u^2, &{}x\in {\mathbb {R}}^3,\end{array}\right.}\end{aligned}$$ 其中 \(\varepsilon \)是一个正参数,f 在无穷远处的 u 中是线性有界的。根据对 V、K 和 f 的适当假设,我们建立了系统的基态解的存在性和渐近行为。我们证明,当 \(\varepsilon \)趋于零时,它们收敛于与经典薛定谔-泊松系统相关的解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solutions of a quasilinear Schrödinger–Poisson system with linearly bounded nonlinearities

Abstract

In this paper, we are concerned with the following quasilinear Schrödinger–Poisson system $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+ K(x)\phi u=f(x,u),\quad &{}x\in {\mathbb {R}}^3,\\ -\Delta \phi -\varepsilon ^4\Delta _4\phi = K(x) u^2, &{}x\in {\mathbb {R}}^3, \end{array}\right. } \end{aligned}$$ where \(\varepsilon \) is a positive parameter and f is linearly bounded in u at infinity. Under suitable assumptions on V, K and f, we establish the existence and asymptotic behavior of ground state solutions to the system. We prove that they converge to the solutions of the classic Schrödinger–Poisson system associated as \(\varepsilon \) tends to zero.

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