Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations

By Dongdong Qin, Vicentiu D. Rădulescu, Xianhua Tang. 2020

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Abstract In this paper, we study the following non-autonomous Choquard-Pekar equation: { − Δ u + V ( x ) u = ( W ⁎ F ( u ) ) f ( u ) , x ∈ R N ( N ≥ 2 ) , u ∈ H 1 ( R N ) , where the potential V ( x ) is 1-periodic and 0 lies in a gap of the spectrum of the Schrodinger operator − Δ + V . Under some general assumptions on the potential W and the nonlinearity f, we show the existence of ground state solutions. We also construct infinitely many geometrically distinct solutions by using the variational method and deformation arguments.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/49c19df353ea17efeae2987cdf9814d0b894b86e