MULTIPLICITY OF SOLUTIONS FOR THE NONLINEAR SCHRODINGER-MAXWELL SYSTEM

In this paper, we study the following system -epsilon(2)Delta v + V(x)v + psi(x)v = v(p), x is an element of R(3), -Delta psi = 1/epsilon v(2), lim(vertical bar x vertical bar -> infinity)psi(x) = 0, x is an element of R(3), where epsilon > 0, p is an element of (3, 5), V is positive potential. We relate the number of solutions with topology of the set where V attain their minimum value. By applying Ljusternik-Schnirelmann theory, we prove the multiplicity of solutions.