Ground state solution and nodal solution for fractional nonlinear Schrödinger equation with indefinite potential

Ground state solution and nodal solution for fractional nonlinear Schrödinger equation with indefinite potential

We prove that under some mild assumptions, the nonlinear fractional Schrödinger equation (−Δ)su+V(x)u=f(u) (x∈RN), where V(x) is an indefinite potential, has two nonzero solutions: one is a positive ground state solution, and the other is a sign-changing solution.

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Veröffentlicht in:Journal of mathematical physics 2019-04, Vol.60 (4)
Hauptverfasser: Li, Yuan, Zhao, Dun, Wang, Qingxuan
Format: Artikel
Sprache:eng
Schlagworte:
Ground state
Physics
Schrodinger equation
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Zusammenfassung:We prove that under some mild assumptions, the nonlinear fractional Schrödinger equation (−Δ)su+V(x)u=f(u) (x∈RN), where V(x) is an indefinite potential, has two nonzero solutions: one is a positive ground state solution, and the other is a sign-changing solution.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.5067377