2022-05-22T17:56:19Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/695042018-04-25T23:44:09Zhdl_2115_45007hdl_2115_116Exponential decay of solutions to nonlinear elliptic equations with potentialsFUKUIZUMI, ReikaOZAWA, Tohru410Exponential decay estimates are obtained for complex-valued solutions to non- linear elliptic equations in Rn, where the linear term is given by Schr odinger operators H = -Δ + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We descrive speci c rates of decay in terms of V , some of which are shown to be optimal. Moreover, our estimates provide a uni ed understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V (x) = |x|2.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69504info:doi/10.14943/83850https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69504/1/pre699.pdfHokkaido University Preprint Series in Mathematics6991122004engpublisher