This paper is devoted to the normalized solutions of a planar L2-critical Schrödinger-Poisson system with an external potential V(x) =❘X❘2 and in-homogeneous attractive interactions K(x)∈(0,1). Applying the constraint variational method, we prove that the normalized solutions exist if and only if the interaction strength a satisfies a∈(0,a*):=∥Q∥2L2(R2), where Q is the unique positive solution of Δu-u u3=0 in R2. Particularly, the re-fined limiting behavior of positive minimizers is also analyzed as a¤a*.
Cite this paper
Xue, Q. (2025). Normalized Solutions for a Planar Schr？dinger-Poisson System with Inhomogeneous Attractive Interactions. Open Access Library Journal, 12, e3315. doi: http://dx.doi.org/10.4236/oalib.1113315.
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