Existence of non-radial sign-changing solutions for asymptotically linear Schrödinger equation on hyperbolic space

In this paper, we are concerned with the existence of non-radial sign-changing solutions for the following stationary nonlinear Schrödinger equation on hyperbolic space: − Δ B N u − λ u = f ( u ) , u ∈ H 1 ( B N ) , where N ≥ 4, λ < ( N − 1 ) 2 4 is a parameter in R and f ∈ C 1 ( R , R ) is asymptotically linear at infinity. By means of an isometric group action on B N and variational methods, we show that the existence of non-radial sign-changing solutions for the subcritical problem.