TY - JOUR
T1 - Least energy radial sign-changing solution for the Schrödinger–Poisson system in R3 under an asymptotically cubic nonlinearity
AU - Murcia, Edwin Gonzalo
AU - Siciliano, Gaetano
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - In this paper we consider the following Schrödinger–Poisson system in the whole R3, {−Δu+u+λϕu=f(u) in R3,−Δϕ=u2 in R3, where λ>0 and the nonlinearity f is “asymptotically cubic” at infinity. This implies that the nonlocal term ϕu and the nonlinear term f(u) are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing the energy functional on the so-called nodal Nehari set.
AB - In this paper we consider the following Schrödinger–Poisson system in the whole R3, {−Δu+u+λϕu=f(u) in R3,−Δϕ=u2 in R3, where λ>0 and the nonlinearity f is “asymptotically cubic” at infinity. This implies that the nonlocal term ϕu and the nonlinear term f(u) are, in some sense, in a strict competition. We show that the system admits a least energy sign-changing and radial solution obtained by minimizing the energy functional on the so-called nodal Nehari set.
KW - Nodal Nehari set
KW - Schrödinger–Poisson system
KW - Standing waves solutions
KW - Variational methods
UR - http://www.scopus.com/inward/record.url?scp=85060972378&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2021.125756
DO - 10.1016/j.jmaa.2021.125756
M3 - Article
AN - SCOPUS:85060972378
SN - 0022-247X
VL - 474
SP - 544
EP - 571
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -