Nodal solutions for a zero-mass Chern-Simons-Schrödinger equation

This study deals with the existence of nodal solutions for the following gauged nonlinear Schr & ouml;dinger equation with zero mass: -Delta u+{(h(u)(2)(divided by x divided by)/(2)(divided by x divided by)+ integral(+infinity)(divided by x divided by)h(u)(s)/(s)u(2)(s)ds}u=divided by u divided by(p-2)u,x is an element of R-2, where p>6 and h(u)(s)=(1)/(2)integral(s)(0)ru(2)(r)dr . By variational methods, we prove that for any integer k >= 0 , the above equation has a nodal solution w(k) which changes sign exactly k times. Moreover, we also prove that w(k) belongs to L-2(R-2) provided p>10 .