TY - JOUR
T1 - Existence of Solutions for Schrodinger-Poisson Systems with Sign-changing Weight
JO - Journal of Partial Differential Equations
VL - 2
SP - 180
EP - 194
PY - 2011
DA - 2011/05
SN - 24
DO - http://doi.org/10.4208/jpde.v24.n2.7
UR - https://global-sci.org/intro/article_detail/jpde/5206.html
KW - Schrödinger-Poisson system
KW - existence result
KW - sign-changing weight
AB - <p>We study the existence of solutions for the Schrödinger-Poisson system $-Δu+u+k(x)φu=α(x)|u|^{p-1}u$, in $R^3$,&nbsp; $-Δφ=k(x)u^2$, in $R^3$, where 3 ≤ p &lt; 5, α(x) is a sign-changing function such that both the supports of α^+ and α^- may have infinite measure. We show that the problem has at least one nontrivial solution under some assumptions.</p>