| Volume 9, Number 5, 2019, Pages 1706-1718 DOI：10.11948/20180273 |
| Infinitely many solutions for a zero mass Schodinger-Poisson-Slater problem with critical growth |
| Liu Yang,Zhisu Liu |
| Keywords:Schrodinger-Poisson-Slater problem, Zero mass, critical growth, concentration-compactness principle. |
| Abstract: |
| In this paper, we are concerned with the following Schr\"{o}dinger-Poisson-Slater problem with critical growth:
$$
-\Delta u+(u^{2}\star \frac{1}{|4\pi x|})u=\mu
k(x)|u|^{p-2}u+|u|^{4}u\,\,\mbox{in}\,\,\R^{3}.
$$
We use a measure representation concentration-compactness principle of Lions to prove that the $(PS)_{c}$ condition holds locally. Via a truncation technique and Krasnoselskii genus theory, we further obtain infinitely many solutions for $\mu\in(0,\mu^{\ast})$ with some $\mu^{\ast}>0$. |
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