Ground states for Schrodinger-Poisson systems with three growth terms
In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V, K, and Q are asymptotically periodic in the va...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/253/abstr.html |
| Summary: | In this article we study the existence and nonexistence
of ground states of the Schrodinger-Poisson system
$$\displaylines{
-\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr
-\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3,
}$$
where V, K, and Q are asymptotically periodic in the variable x.
The proof is based on the the method of Nehari manifold and concentration
compactness principle. In particular, we develop the method of Nehari manifold
for Schrodinger-Poisson systems with three times growth. |
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| ISSN: | 1072-6691 |