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中文摘要：
利用Ekeland＇s变分原理和山路引理,考虑合作型拟线性椭圆系统-Δpu=λa（x）｜u｜p-2u＋λ/β＋1b（x）｜u｜α｜v｜βv＋Fu（x,u,v）,x∈Ω;-Δqu=λc（x）｜v｜q-2v＋λ/α＋1b（x）｜u｜α｜v｜βu＋Fv（x,u,v）,x∈Ω;u=v=0,x∈Ω在参数λ从左边无限接近于相应的非线性特征值问题的第一个特征值λ1时,系统有3个非平凡解.
英文摘要：
By using Ekeland＇s variational principle and Mountain Pass Theorem in critical point theory,for λλ1 sufficiently close to λ1,where λ1 is the first eigenvalue of the corresponding nonlinear eigenvalue problem,the following cooperative quasilinear elliptic systems{-Δpu=λa（x）｜u｜p-2u＋λ/β＋1b（x）｜u｜α｜v｜βv＋Fu（x,u,v）,x∈Ω;-Δqu=λc（x）｜v｜q-2v＋λ/α＋1b（x）｜u｜α｜v｜βu＋Fv（x,u,v）,x∈Ω;u=v=0,x∈Ω has three nontrivial solutions.
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