On multiplicity and concentration of solutions for a gauged nonlinear Schrödinger equation

This paper is concerned with a gauged nonlinear Schrodinger equation -Delta u + lambda V(vertical bar x vertical bar)u + (h(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) + integral(infinity)(vertical bar x vertical bar) h(s)/s u(2)(s)ds) u = f (vertical bar x vertical bar, u) in R-2, where V is a external potential and. is a positive parameter. We assume that the potential has a bounded potential well and the nonlinearity is sublinear at infinity, the existence and multiplicity results of solutions are obtained by using the genus properties in critical point theory. Moreover, the concentration behavior of solutions on the potential well is also explored.