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Ground state solutions for a class of nonlinear fractional Schrödinger-Poisson systems with super-quadratic nonlinearity. (English) Zbl 1380.35160

Summary: We consider the existence of ground state solutions for a class of nonlinear fractional Schrödinger-Poisson systems of the form \[ \begin{cases} (-\Delta)^su+u+\phi u=f(u),\quad & \text{in }\mathbb R^3,\\ (-\Delta)^t\phi=u^2,\quad & \text{in }\mathbb R^3,\end{cases} \] where \(0<s\leq t<1\) and \(2s+2t>3\). By adopting a direct approach and the Pohozaev identity, we prove that this system possesses ground state solutions with a mild assumption on \(f\) with \(\lim_{|u|\to\infty}\frac{\int^u_0 f(t)dt}{|u|^3}=\infty\).

MSC:

35R11 Fractional partial differential equations
58E30 Variational principles in infinite-dimensional spaces
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