%0 Journal Article
%T Normalized Solutions for a Planar Schr£¿dinger-Poisson System with Inhomogeneous Attractive Interactions<br />
%A Qi Xue
%J Open Access Library Journal
%V 12
%N 4
%P 1-14
%@ 2333-9721
%D 2025
%I Open Access Library
%R 10.4236/oalib.1113315
%X This paper is devoted to the normalized solutions of a planar <em>L</em><sup>2</sup>-critical Schr&#246;dinger-Poisson system with an external potential <em>V</em>(x) =&#10072;X&#10072;<sup>2</sup> and in-homogeneous attractive interactions <i>K</i>(x)¡Ê(0,1). Applying the constraint variational method, we prove that the normalized solutions exist if and only if the interaction strength <i>a</i> satisfies <i>a</i>¡Ê(0,a<sup>*</sup>):=¡ÎQ¡Î<sup>2</sup><sub>L<sup>2</sup>(R<sup>2</sup>)</sub>, where Q is the unique positive solution of ¦¤u-u u<sup>3</sup>=0 in R<sup>2</sup>. Particularly, the re-fined limiting behavior of positive minimizers is also analyzed as a¡èa<sup>*</sup>.<br />
%K Schr&#246
%K dinger-Poisson System
%K Logarithmic Convolution
%K Inhomogeneous Attractive Interaction
%K Normalized Solution
%U http://www.oalib.com/paper/6857150