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

Abstract

The present study is concerned with the following Schrödinger-Poisson system involving critical nonlocal term with general nonlinearity: $$\{\begin{array}{llc}-\Delta u+V(x)u-\varphi |u{|}^{3}u=f(u),& x\in {\mathbb{R}}^3,-\Delta \varphi =|u{|}^5,& x\in {\mathbb{R}}^3,\end{array}$$ 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 Pohožaev type manifold. In particular, the Ambrosetti-Rabinowitz type condition or monotonicity assumption on the nonlinearity is not necessary.

arXiv admin note: text overlap with arXiv:1702.03792

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