Multiple solutions for Schrodinger-Poisson systems with sign-changing potential and critical nonlinearity
In this article, we study the Schr\"odinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+k(x)\phi(x)u=h_1(x)|u|^{4}u+\mu h_{2}(x)u+h_3(x), \quad\text{in } \mathbb{R}^3, \cr -\Delta \phi(x)=k(x)u^2 , \quad\text{in } \mathbb{R}^3, }$$ where $h_1(x),h_{2}(x),h_3(x), V(x)$ are allowed to b...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-10-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/276/abstr.html |
| Summary: | In this article, we study the Schr\"odinger-Poisson system
$$\displaylines{
-\Delta u+V(x)u+k(x)\phi(x)u=h_1(x)|u|^{4}u+\mu h_{2}(x)u+h_3(x),
\quad\text{in } \mathbb{R}^3, \cr
-\Delta \phi(x)=k(x)u^2 , \quad\text{in } \mathbb{R}^3,
}$$
where $h_1(x),h_{2}(x),h_3(x), V(x)$ are allowed to be sign-changing
and $\mu>0$ is a parameter. Under some appropriate assumptions on V(x),
we obtain the existence of two different solutions for the above system
via variational methods. |
|---|---|
| ISSN: | 1072-6691 |