Nodal Type Bound States for Nonlinear Schrödinger Equations with Decaying Potentials
Year: 2012
Author: Tingjian Luo, Zhengping Wang
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 79–89
Abstract
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∈RN,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].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v25.n1.6
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 79–89
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: Nonlinear Schrödinger equation
Author Details
Tingjian Luo Email
Zhengping Wang Email