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In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems
-Dα (aαβ(x,u) Dβui) + 1/2 Dui
aαβ(x,u)Dαuj Dβuj + h(x) ui =
λ|u|
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