Geodesic
Existence results for strongly indefinite elliptic systems
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we show the existence of solutions for the strongly indefinite elliptic system $$\displaylines{ -\Delta u=\lambda u+f(x,v) \quad\hbox{in }\Omega, \cr -\Delta v=\lambda v+g(x,u) \quad\hbox{in }\Omega, \cr u=v=0, \quad\hbox{on }\partial\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N\; (N\geq 3)$ with smooth boundary, $\lambda_{k_0}\lambda\lambda_{k_0+1}$, where $\lambda_k$ is the $k$th eigenvalue of $-\Delta$ in $\Omega$ with zero Dirichlet boundary condition. Both cases when $f,g$ being superlinear and asymptotically linear at infinity are considered.
Classification : 35J20
Keywords: strongly indefinite elliptic system, existence 
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     author = {Yang, Jianfu and Ye, Ying and Yu, Xiaohui},
     title = {Existence results for strongly indefinite elliptic systems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a95/}
}
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Yang, Jianfu; Ye, Ying; Yu, Xiaohui. Existence results for strongly indefinite elliptic systems. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a95/