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Remarks on a dispersive equation in de Sitter spacetime

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  • Some nonlinear Schrödinger equations are derived from the nonrelativistic limit of nonlinear Klein-Gordon equations in de Sitter spacetime. Time local solutions for the Cauchy problem are considered in Sobolev spaces for power type nonlinear terms. The roles of spatial expansion and contraction on the problem are studied.
    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35L70.


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