(untitled) (Journal of Partial Differential Equations, 2012)
In this paper, we are concerned with the existence of nodal type bound state for the following stationary nonlinear Schrödinger equation -Δu(x)+V(x)u(x)=|u|^p-1u, x∈ R^N, N ≥ 3, where 1 < p < (N+2)/(N-2) and the potential V(x) is a positive radial function and may decay to zero at infinity. Under appropriate assumptions on the decay rate of V(x), Souplet and Zhang [1] proved the above equation has a positive bound state. In this paper, we construct a nodal solution with precisely two nodal domains and prove that the above equation has a nodal type bound state under the same conditions on V(x) as in [1].