摘要

We study the following coupled Schrodinger equations which have appeared as several models from mathematical physics: {-Delta u(1) + lambda(1)u(1) = mu(1)u(1)(3) + beta u(1)u(2)(2), x is an element of Omega, -Delta u(2) + lambda(2)u(2) = mu(2)u(2)(3) + beta u(1)u(2)(2), x is an element of Omega, u(1) = u(2) = 0 on partial derivative Omega. Here Omega subset of R-N (N = 2,3) is a smooth bounded domain, lambda(l), lambda(2), mu(1), mu(2) are all positive constants. We show that, for each k is an element of N there exists beta(k) > 0 such that this system has at least k sign-changing solutions (i.e., both two components change sign) and k semi-nodal solutions (i.e., one component changes sign and the other one is positive) for each fixed beta is an element of (0, beta(k)).

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