부산대학교 도서관

This paper deals with a class of fractional Schrödinger‐Poisson system (−Δ)su+V(x)u−K(x)ϕ|u|2s∗−3u=a(x)f(u),x∈ℝ3(−Δ)sϕ=K(x)|u|2s∗−1,x∈ℝ3$$ \left\{\begin{array}{cc}{\left(-\Delta \right)}^su+V(x)u-K(x)\phi {\left|u\right|}^{2_s^{\ast }-3}u=a(x)f(u),\kern0.30em & x\in {\mathbb{R}}^3\\ {}{\left(-\Delta \right)}^s\phi =K(x){\left|u\right|}^{2_s^{\ast }-1},\kern0.30em & x\in {\mathbb{R}}^3\end{array}\right. $$with a critical nonlocal term and multiple competing potentials, which may decay and vanish at infinity, where s∈(34,1),2s∗=63−2s$$ s\in \left(\frac{3}{4},1\right),{2}_s^{\ast }=\frac{6}{3-2s} $$ is the fractional critical exponent. The problem is set on the whole space, and compactness issues have to be tackled. By employing the mountain pass theorem, concentration‐compactness principle, and approximation method, the existence of a positive ground state solution is obtained under appropriate assumptions imposed on V$$ V $$, K$$ K $$, a$$ a $$, and f$$ f $$. [ABSTRACT FROM AUTHOR]