Geodesic
Existence results for strongly indefinite elliptic systems
Electronic journal of differential equations, Tome 2008 (2008)
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 
@article{EJDE_2008__2008__a95,
     author = {Yang,  Jianfu and Ye,  Ying and Yu,  Xiaohui},
     title = {Existence results for strongly indefinite elliptic systems},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1173.35454},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a95/}
}
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AU  - Yu,  Xiaohui
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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/