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Improved results for Klein-Gordon-Maxwell systems with general nonlinearity

This work is partially supported by the Hunan Provincial Innovation Foundation for Postgraduate (No: CX2017B041) and the National Natural Science Foundation of China (No: 11571370)

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  • This paper is concerned with the following Klein-Gordon-Maxwell system

    $\left\{ \begin{align} &-\vartriangle u+\left[ m_{0}^{2}-{{(\omega +\phi )}^{2}} \right]u = f(u),\ \ \ \ \text{in}\ \ {{\mathbb{R}}^{3}}, \\ &\vartriangle \phi = (\omega +\phi ){{u}^{2}},\ \ \ \ \text{in}\ \ {{\mathbb{R}}^{3}}, \\ \end{align} \right.$

    where $0 < ω≤ m_0$ and $f∈ \mathcal{C}(\mathbb{R}, \mathbb{R})$. By introducing some new tricks, we prove that the above system has 1) a ground state solution in the case when $0 < ω < m_0$ and $f$ is superlinear at infinity; 2) a nontrivial solution in the zero mass case, i.e. $ω = m_0$ and $f$ is super-quadratic at infinity. These results improve the related ones in the literature.

    Mathematics Subject Classification: 35J10, 35J20.


    \begin{equation} \\ \end{equation}
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