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The number of nodal solutions for the Schrödinger–Poisson system under the effect of the weight function

  • * Corresponding author: Tsung-fang Wu

    * Corresponding author: Tsung-fang Wu

J. Sun is supported by the National Natural Science Foundation of China (Grant No. 11671236). T.F. Wu is supported in part by the Ministry of Science and Technology, Taiwan (Grant 108-2115-M-390-007-MY2)

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  • In this paper, we study the multiplicity of two spikes nodal solutions for a nonautonomous Schrödinger–Poisson system with the nonlinearity $ f(x)\vert u\vert ^{p-2}u(2<p<6) $ in $ \mathbb{R}^{3} $. By assuming that the weight function $ f\in C(\mathbb{R}^{3},\mathbb{R}^{+}) $ has $ m $ maximum points in $ \mathbb{R}^{3} $, we conclude that such system admits $ m^{2} $ distinct nodal solutions, each of which has exactly two nodal domains. The proof is based on a natural constraint approach developed by us as well as the generalized barycenter map.

    Mathematics Subject Classification: Primary: 35J20; Secondary: 35J61, 35Q40.


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