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

This paper discusses the quasilinear Schrödinger equation −Δu+V(x)u−Δ[(1+u2)12]u2(1+u2)12=K(x)f(u),x∈RN,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.