Normalized Solutions for Fractional Schrödinger–Poisson System with General Nonlinearities

Existence of normalized solutions for fractional Kirchhoff–Schrödinger–Poisson equations with general nonlinearities

“…Moreover, by using Pohozaev manifold and variational method, Li and Teng [15] expanded the above results to the following fractional Schrödinger-Poisson system:…”

“…Yang et al [25] used the same method to study the existence of normalized solutions to the following Kirchhoff–Schrödinger–Poisson system: $$$$ \left\{\begin{array}{lll}& -\left(a+b{\int}_{{\mathrm{\mathbb{R}}}^3}{\left|\nabla u\right|}^2\mathrm{d}x\right)\Delta u+\phi u=f(u)+\lambda u& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}^3,\\ {}& -\Delta \phi ={u}^2& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}^3.\end{array}\right. $$$$ Moreover, by using Pohozaev manifold and variational method, Li and Teng [15] expanded the above results to the following fractional Schrödinger–Poisson system: $$$$ \left\{\begin{array}{lll}& {\left(-\Delta \right)}^{\alpha }u+\phi u=f(u)+\lambda u& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}^3,\\ {}& {\left(-\Delta \right)}^{\beta}\phi ={u}^2& \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}^3,\end{array}\right. $$$$…”