1 results
Existence of solutions for a semilinear ellipticsystem
-
- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 2 / April 2013
- Published online by Cambridge University Press:
- 15 February 2013, pp. 574-586
- Print publication:
- April 2013
-
- Article
- Export citation
-
This paper deals with the existence of solutions to the following system:
$$\left\{\begin{array}{l} -\Deltau+u=\frac{\alpha}{\alpha+\beta}a(x)|v|^{\beta} |u|^{\alpha-2}u\quad\mbox{ in}\mathbb{R}^N\\ [0.2cm] -\Delta v+v=\frac{\beta}{\alpha+\beta}a(x)|u|^{\alpha}|v|^{\beta-2}v\quad\mbox{ in }\mathbb{R}^N. \end{array}\right.$$
With the help of the Nehari manifold and the linking theorem, we prove the existence ofat least two nontrivial solutions. One of them is positive. Our main tools are theconcentration-compactness principle and the Ekeland’s variational principle.
