GROUND STATE RADIAL SIGN-CHANGING SOLUTIONS FOR A GAUGED NONLINEAR SCHRODINGER EQUATION INVOLVING CRITICAL GROWTH

We investigate the following gauged nonlinear Schrodinger equation {-Delta u + omega u + lambda(h(u)(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) + integral(+infinity)(vertical bar x vertical bar) h(u)(s)/s u(2)(s)ds)u = f(u) in R-2, u is an element of H-r(1) (R-2), where omega, lambda > 0 and h(u)(s) = 1/2 integral(s)(0) ru(2)(r)dr. When f has exponential critical growth, by using the constrained minimization method and Trudinger-Moser inequality, it is proved that the equation has a ground state radial sign-changing solution u(lambda) which changes sign exactly once. Moreover, the asymptotic behavior of u(lambda) as lambda -> 0 is analyzed.