Revisit to sign-changing solutions for the nonlinear Schrödinger–Poisson system in R3

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Abstract

In this paper, we investigate the existence of solutions for the nonlinear Schrödinger–Poisson system with zero mass. By introducing some new ideas, we prove, via the constraint variational method and the quantitative deformation lemma, that the system has a sign-changing solution.

Keywords

Schrödinger–Poisson system
Sign-changing solution
Zero mass

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Partially supported by National Natural Science Foundation of China (Grant Nos. 11301313, 11571209), Science Council of Shanxi Province (2013021001-4, 2014021009-1, 2015021007).