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arXiv · 1710.09120

Uniqueness and symmetry of ground states for higher-order equations

Woocheol Choi·Younghun Hong·Jinmyoung Seok
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Abstract

We establish uniqueness and radial symmetry of ground states for higher-order nonlinear Schr\"odinger 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 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 to construct radially symmetric real-valued solutions, as well as improving local uniqueness near the limit.

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Woocheol Choi, Younghun Hong, Jinmyoung Seok. 2017-10-25. Uniqueness and symmetry of ground states for higher-order equations. https://arxiv.org/abs/1710.09120

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