Uniqueness and nondegeneracy of ground states for the Schrödinger-Newton equation with power nonlinearity

2023/12/01 by Luo, Huxiao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.00465

Abstract

In this article, we study the Schrödinger-Newton equation -Δu+λu=(1)/(4π)((1)/(|x|)⋆ u²)u+|u|^q-2u in~ℝ³, where λ∈ℝ₊, q∈ (2,3)∪(3, 6). By investigating limit profiles of ground states as λ→0⁺ or λ→+∞, we prove the uniqueness of ground states. By the action of the linearized eqaution with respect to decomposition into spherical harmonics, we obtain the nondegeneracy of ground states.

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