中文摘要：

Schrodinger方程-△u＋λ2u=｜u｜2q-2u有唯一的正径向对称解Uλ，当r→∞时Uλ指数衰减到零．因此可以预料薛定谔方程组-△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2存在在某些点附近形同Uλ的多峰解．对于u=（u1，u2）∈H1（R3）×H1（R3）定义非线性泛函Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,其中I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx,I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx.证明了此泛函的临界点就是薛定谔方程组的解．设Z为非扰动问题的解流形，TzZ为此流形的切空间．寻求Iε的形如z＋w的临界点，其中W∈（TzZ）⊥．应用Iε的性质，证明了Lε在近似于（n∑i=1U（x-ξi）,n∑i=1V（x-ξi）1的多峰解．

英文摘要：

The Schrodinger equation -△u＋λ2u=｜u｜2q-2u has a unique positive radial solution Uλ, which decays exponentially at infinity. Hence it is reasonable that the Schrolinger system -△u1＋u1=｜u1｜2q-1u1-εb（x）｜u2｜1｜u1｜q-1u1,-△u2＋u2=｜u2｜2q-2u2-εb（x）｜u1｜1｜u2｜q-1u2 has multiple-bump solutions which behave like Uλ in the neighborhood of some points. For u=（u1,u2）∈H1（R3）×H1（R3）, a nonlinear functional Iε（u）=I1（u1）＋I2（u2）-ε/q∫R3b（x）｜u1｜q｜u2｜qdx,is defined,where I1（u1）=1/2｜｜u1｜｜2-1/2q∫R3｜u1｜2qdx and I2（u2）=1/2｜｜u2｜｜2ω-1/2q∫R3｜u2｜2qdx. It is proved that the solutions of the system are the critical points of I,. Let Z be the smooth solution manifold of the unperturbed problem and TzZ is the tangent space. The critical point of I is rewritten as the form of z ＋ w, where w ∈ （TzZ）⊥. Using some properties of Iε, it is proved that there exists a critical point of I, close to the form which is a multi-bump solution.