Infinitely many solutions to a quasilinear Schrodinger equation with a local sublinear term

This paper discusses the quasilinear Schrodinger equation -Delta u + V(x)u - Delta[(1+u(2))(1/2)] u/2(1 + u(2))(1/2) = K(x) f(x), x is an element of R-N, where N >= 3. Under appropriate assumptions on the potentials V and K and local sublinear growth assumptions on the nonlinear term f, we get the existence of infinitely many nontrivial solutions by using a revised Clark theorem and a priori estimate of the solution. (C) 2018 Elsevier Ltd. All rights reserved.