Sign-changing solutions to a gauged nonlinear Schrodinger equation

We study the existence and asymptotic behavior of the least energy sign-changing solutions to a gauged nonlinear Schrodinger equation {-Delta u + omega u + lambda(h2 vertical bar x vertical bar)/vertical bar x vertical bar(2) + (vertical bar x vertical bar)integral(+infinity) h(s)/su(2)(s)ds)u = vertical bar u vertical bar(p-2)u, x is an element of R-2, u is an element of H-r(1)(R-2), where omega, lambda > 0, p > 6 and h(s) = 1/2 (0)integral(s) ru(2)(r)dr. Combining constraint minimization method and quantitative deformation lemma, we prove that the problem possesses at least one least energy sign -changing solution u(lambda), which changes sign exactly once. Moreover, we show that the energy of u(lambda) is strictly larger than two times of the ground state energy. Finally, the asymptotic behavior of u(lambda) as lambda SE arrow 0 is also analyzed. (C) 2017 Elsevier Inc. All rights reserved.