2023-03-22T19:31:03Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/695052022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Stability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearitiesDE BOUARD, AnneFUKUIZUMI, Reikaopen access410The effect of inhomogenity of nonlinear medium is discussed concerning the stability of standing waves eiωtφω(x) for a nonlinear Schrödinger equation with an inhomogeneous nonlinearity V (x)|u|p-1u, where V(x) is proportional to the electron density. Here, ω > 0 and φω(x) is a ground state of the stationary problem. When V(x) behaves like |x|-b at in nity, where 0 < b < 2, we show that eiωtφω(x) is stable for p < 1 + (4 - 2b)=n and sufficiently small ω > 0. The main point of this paper is to analyze the linearized operator at standing wave solution for the case of V (x) = |x|-b. Then, this analysis yields a stability result for the case of more general, inhomogeneous V (x) by a certain perturbation method.Department of Mathematics, Hokkaido University2004engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83851http://hdl.handle.net/2115/6950510.14943/83851Hokkaido University Preprint Series in Mathematics700118https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69505/1/pre700.pdfapplication/pdf141.7 KB2004