科研之友
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摘要
In this paper, we study the following nonlinear Schrodinger-Newton system ?delta u-V(x)u+Psi u=0, x is an element of R-3,R- delta Psi+(1)/(2)u(2)=0, x is an element of R-3,which is a nonlinear system obtained by coupling the linear Schrodinger equation of quantum mechanics with the gravitation law of Newtonian mechanics. Assuming that V(y) is radial and satisfies some algebraic decay at the infinity, we construct infinitely many non-radial positive solutions which have polygonal symmetry with respect to y(1)and y(2) and are even in y(2) for the system above by the Lyapunov-Schmidt reduction method. Moreover, we have overcame some new difficulties caused by the non-local term.
