4,912 research outputs found
Schr\"odinger-Poisson equations with singular potentials in
The existence and estimate of positive solutions are discussed
for the following Schr\"{o}dinger-Poisson system {ll} -\Delta u
+(\lambda+\frac{1}{|y|^\alpha})u+\phi (x) u =|u|^{p-1}u, x=(y,z)\in
\mathbb{R}^2\times\mathbb{R}, -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow
+\infty}\phi(x)=0, \hfill y=(x_1,x_2) \in \mathbb{R}^2 with
|y|=\sqrt{x_1^2+x_2^2}, where , and
.Comment: 23page
- …