On nonlinear Schrödinger equations derived from the nonrelativistic limit of nonlinear Klein–Gordon equations in de Sitter spacetime

Some Schrödinger equations with weighted nonlinear terms are derived from the nonrelativistic limit of nonlinear Klein–Gordon equations in de Sitter spacetime. Local and global solutions for the Cauchy problem are considered in Sobolev spaces for power type and exponential type nonlinear terms. The roles of spatial expansion and contraction on the problem are studied. And a dissipative property of the equations is remarked.