TY - JOUR
T1 - Nodal Type Bound States for Nonlinear Schrödinger Equations with Decaying Potentials
AU - Luo , Tingjian
AU - Wang , Zhengping
JO - Journal of Partial Differential Equations
VL - 1
SP - 79
EP - 89
PY - 2012
DA - 2012/03
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/5176.html
KW - Nonlinear Schrödinger equation
KW - nodal type bound state
KW - decaying potential
AB - <p>In this paper, we are concerned with the existence of nodal type bound state for the following stationary nonlinear Schrödinger equation $$-Δu(x)+V(x)u(x)=|u|^{p-1}u, x∈ R^N, N ≥ 3,$$ where 1 &lt; p &lt; (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].</p>