On degenerate fractional Schrödinger-Kirchhoff-Poisson equations with upper critical nonlinearity and electromagnetic fields

We investigate the degenerate fractional Schrödinger-Kirchhoff-Poisson equation in ${\mathbb{R}}^3$ with critical nonlinearity and electromagnetic fields ${\epsilon }^{2s}M([u{]}_{s,A}^2)(-\mathrm{\Delta }{)}_A^{s}u+V(x)u+\phi u=k(x)\mathrm{\mid }u{\mathrm{\mid }}^{r-2}u+({\mathcal{I}}_{\mu }\ast \mathrm{\mid }u{\mathrm{\mid }}^{2_s^{\mathrm{♯}}})\mathrm{\mid }u{\mathrm{\mid }}^{2_s^{\mathrm{♯}}-2}u$ and $(-\mathrm{\Delta }{)}^t\phi =u^2,$ where $\epsilon >0$ is a parameter, $3\mathrm{/}4<s<1$, $0<t<1$, $V$ is an electric potential satisfying some suitable assumptions, $0<k_{\ast }\le k(x)\le k^{\ast }$, ${\mathcal{I}}_{\mu }(x)=\mathrm{\mid }x{\mathrm{\mid }}^{3-\mu }$ with $0<\mu <3$, $2_s^{\mathrm{♯}}=\frac{3+\mu }{3-2s},$ and $2<r<2_s^{\mathrm{♯}}$. With the help of the concentration compactness principle and variational methods, together with some fine analytical tools, we establish the existence and multiplicity of solutions for the above problem when $\epsilon \to 0$ in the degenerate cases, i.e. when the Kirchhoff term $M$ vanishes at zero.