Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term

Liejun Shen; Xiaohua Yao

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arXiv · 1702.03792

Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term

Liejun Shen·Xiaohua Yao

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Abstract

The present study is concerned with the following Schrödinger-Poisson system involving critical nonlocal term $$ \left\{ \begin{array}{ll} -Δu+u-K(x)ϕ|u|^3u=λf(x)|u|^{q-2}u, & x\in\mathbb{R}^3, -Δϕ=K(x)|u|^5, & x\in\mathbb{R}^3,\\ \end{array} \right. $$ where $1 0$ is a parameter. Under suitable assumptions on $K(x)$ and $f(x)$, there exists $λ_0=λ_0(q,S,f,K)>0$ such that for any $λ\in(0,λ_0)$, the above Schrödinger-Poisson system possesses at least two positive solutions by standard variational method, where a positive least energy solution will also be obtained.

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BibTeX RIS

Liejun Shen, Xiaohua Yao. 2017-02-13. Multiple positive solutions for Schrodinger-Poisson systems involving critical nonlocal term. https://arxiv.org/abs/1702.03792

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