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Normalized ground state solutions for the Schrödinger systems with critical exponential growth in R2Chen, Jing; Xie, Zheng; Zhang, Xinghua
Journal of mathematical analysis and applications, 12/2024, Letnik: 540, Številka: 1Journal Article
In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with critical exponential growth:{−Δu+λ1u=f1(u)+βr1|u|r1−2u|v|r2,inR2,−Δv+λ2v=f2(v)+βr2|u|r1|v|r2−2v,inR2,∫R2u2dx=a2and∫R2v2dx=b2,u,v∈H1(R2), where 0<a,b<1,β>0,r1,r2>1 and r1+r2∈(4,+∞), f1,f2∈C(R,R) have critical exponential growth in the sense of Trudinger-Moser inequality. λ1,λ2∈R will arise as Lagrange multipliers. Under some suitable assumptions on f1,f2, we prove the existence of positive normalized ground state solutions for the problem when β>0 is sufficiently large via variational method. Our results improve and extend the previous results.
