Existence of normalized solutions for the planar Schrödinger-Poisson system with exponential critical nonlinearity

2021/07/28 by Alves, Claudianor O., Boër, Eduardo de S., Miyagaki, Olímpio H. · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.13281

Abstract

In the present work we are concerned with the existence of normalized solutions to the following Schrödinger-Poisson System \ -Δu + λu + μ(ln|⋅|∗ |u|²)u = f(u) \textrm in ℝ² ,
\intR |u(x)|² dx = c, c · gt; 0 , . for μ∈ \R and a nonlinearity f with exponential critical growth. Here λ∈ \R stands as a Lagrange multiplier and it is part of the unknown. Our main results extend and/or complement some results found in \citeJi and \cite[cjj].

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• On planar Schrodinger-Poisson systems with repulsive interactions in the mass supercritical regime

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