Volume 24, Issue 2
Existence of Solutions for Schrodinger-Poisson Systems with Sign-changing Weight

J. Part. Diff. Eq., 24 (2011), pp. 180-194.

Published online: 2011-05

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• Abstract

We study the existence of solutions for the Schrödinger-Poisson system $-Δu+u+k(x)φu=α(x)|u|^{p-1}u$, in $R^3$,  $-Δφ=k(x)u^2$, in $R^3$, where 3 ≤ p < 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.

• Keywords

Schrödinger-Poisson system existence result sign-changing weight

35J60 35J20

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@Article{JPDE-24-180, author = {}, title = {Existence of Solutions for Schrodinger-Poisson Systems with Sign-changing Weight}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {2}, pages = {180--194}, abstract = {

We study the existence of solutions for the Schrödinger-Poisson system $-Δu+u+k(x)φu=α(x)|u|^{p-1}u$, in $R^3$,  $-Δφ=k(x)u^2$, in $R^3$, where 3 ≤ p < 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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n2.7}, url = {http://global-sci.org/intro/article_detail/jpde/5206.html} }
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 -

We study the existence of solutions for the Schrödinger-Poisson system $-Δu+u+k(x)φu=α(x)|u|^{p-1}u$, in $R^3$,  $-Δφ=k(x)u^2$, in $R^3$, where 3 ≤ p < 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.

Xiaohui Yu . (2019). Existence of Solutions for Schrodinger-Poisson Systems with Sign-changing Weight. Journal of Partial Differential Equations. 24 (2). 180-194. doi:10.4208/jpde.v24.n2.7
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