The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity

Liejun Shen; Xiaohua Yao

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arXiv · 1702.03785

The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity

Liejun Shen·Xiaohua Yao

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Abstract

The present study is concerned with the following Schr\"{o}dinger-Poisson system involving critical nonlocal term with general nonlinearity: $$ \left\{ \begin{array}{ll} -\Delta u+V(x)u- \phi |u|^3u= f(u), & x\in\mathbb{R}^3, -\Delta \phi= |u|^5, & x\in\mathbb{R}^3,\\ \end{array} \right. $$ Under certain assumptions on non-constant $V(x)$, the existence of a positive least energy solution is obtained by using some new analytical skills and Poho\v{z}aev type manifold. In particular, the Ambrosetti-Rabinowitz type condition or monotonicity assumption on the nonlinearity is not necessary.

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Liejun Shen, Xiaohua Yao. 2017-02-13. The existence of positive least energy solutions for a class of Schrodinger-Poisson systems involving critical nonlocal term with general nonlinearity. https://arxiv.org/abs/1702.03785

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