Uniqueness and symmetry of ground states for higher-order equations |
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Authors: | Woocheol?Choi Email author" target="_blank">Younghun?HongEmail author Jinmyoung?Seok |
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Institution: | 1.Department of Mathematics Education,Incheon National University,Incheon,Republic of Korea;2.Department of Mathematics,Chung-Ang University,Seoul,Republic of Korea;3.Department of Mathematics,Kyonggi University,Suwon,Republic of Korea |
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Abstract: | We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schrödinger and Hartree equations whose higher-order differentials have small coefficients. As an application, we obtain error estimates for higher-order approximations to the pseudo-relativistic ground state. Our proof adapts the strategy of Lenzmann (Anal PDE 2:1–27, 2009) using local uniqueness near the limit of ground states in a variational problem. However, in order to bypass difficulties from lack of symmetrization tools for higher-order differential operators, we employ the contraction mapping argument in our earlier work (Choi et al. 2017. arXiv:1705.09068) to construct radially symmetric real-valued solutions, as well as improving local uniqueness near the limit. |
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