Odd symmetry of least energy nodal solutions for the Choquard equation

By D. Ruiz, Jean Van Schaftingen. 2016

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Abstract We consider the Choquard equation (also known as the stationary Hartree equation or Schrodinger–Newton equation) − Δ u + u = ( I α ⁎ | u | p ) | u | p − 2 u . Here I α stands for the Riesz potential of order α ∈ ( 0 , N ) , and N − 2 N + α 1 p ≤ 1 2 . We prove that least energy nodal solutions have an odd symmetry with respect to a hyperplane when α is either close to 0 or close to N.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5f5cfdd11f11f406f8ec012a7a984df40b6fbd92