Existence of sign-changing solutions for a gauged nonlinear Schrodinger equation with a quintic term

In this paper, we study the existence and asymptotic behavior of sign-changing solutions with arbitrary number of nodes to the following gauged nonlinear Schrodinger equation {- Delta u+ omega u +((h(u)(vertical bar x vertical bar))(2)/vertical bar x vertical bar(2) + integral(vertical bar x vertical bar) (+infinity) h(u)(s)/s u(2)(s)ds)u = lambda vertical bar u vertical bar(4)u in R-2, (0.1) u is an element of H-1(R)(2) where omega, lambda > 0 and h(u)(s) -1/2 integral(s)(0) ru(2)(r)dr is the so-called Chern-Simons term. The nonlocal term g(u) := ((h(u)(vertical bar x vertical bar))(2)/vertical bar x vertical bar(2) + integral(+infinity)(vertical bar x vertical bar) h(u)(s)/u(2)(s)ds)u is quintic in the sense that g(tu) = t(5)g(u), which is in complicated competition with the nonlinear term lambda vertical bar u vertical bar(4)u. This causes that not all functions in H-1(R-2) can be projected onto the usual Nehari manifold, and so the classical Nehari manifold method is not applicable. By taking advantage of the Miranda theorem and Gersgorin disc theorem, via the variational method and gluing approach, we prove that for each positive integer k, the problem (0.1) admits a radial sign-changing solution U-k,6(lambda) that changes sign exactly k times. Moreover, its energy is strictly increasing in k, and for any sequence {lambda(n)} with lambda(n) -> vertical bar infinity, up to a subsequence, lambda(1/4)(n) U-k,6(lambda n) converges to some (U) over bar (0)(k,6) is an element of H-1(R-2) which is a radial sign-changing solution with exactly k nodes to the following local equation {- Delta u + omega u = vertical bar u vertical bar(4)u in R-2, u is an element of H-1(R-2). Our results extend the existing ones of [6] from the super-quintic case to the quintic case. (c) 2022 Elsevier Inc. All rights reserved.