Abstract
We investigate normalized solutions to the planar Schrödinger–Poisson systems with square-root nonlinearity −Δu+λu+12π(log|⋅|∗|u|2)u=1−11+u2uinR2,∫R2|u|2dx=c,where λ∈R appears as a Lagrange parameter and c>0 is a given real number. We prove the existence of normalized solutions by establishing a new estimate on the square-root nonlinearity.
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