@Article{JPDE-25-79,
author = {Luo , Tingjian and Wang , Zhengping},
title = {Nodal Type Bound States for Nonlinear Schrödinger Equations with Decaying Potentials},
journal = {Journal of Partial Differential Equations},
year = {2012},
volume = {25},
number = {1},
pages = {79--89},
abstract = {<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>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v25.n1.6},
url = {http://global-sci.org/intro/article_detail/jpde/5176.html}
}