Yiwei Ye: Ground state solutions for nonautonomous Schrödinger-Poisson systems involving critical exponent, 199-207

Abstract:

For the Schrödinger-Poisson system with critical exponent of the version $-\Delta u+V(x)u+\phi u=a(x)f(u)+u^5$ in $\mathbb{R}^3$ and $-\Delta \phi=u^2$ in $\mathbb{R}^3$, we prove the existence of one ground state solution when $\lim_{\vert x\vert\rightarrow \infty}V(x)=V_\infty>0$ and $V(x)\leq V_\infty+C_1e^{-b\vert x\vert}$ for some $b>0$ and $\vert x\vert$ large.

Key Words: Schrödinger-Poisson system, critical growth, variational methods

2010 Mathematics Subject Classification: Primary 35J47; Secondary 35J50.