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Schrödinger-Poisson systems in $4$-dimensional closed manifolds

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  • We investigate existence, nonexistence and uniqueness of positive solutions of critical Schrödinger-Poisson systems in closed $4$-manifolds. In the process we provide a sharp criterion for the non-existence of resonant states.
    Mathematics Subject Classification: Primary: 58J05; Secondary: 35J47, 35Q61, 35R01, 58J37, 81Q35.


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