Existence and symmetric result for Liouville-Weyl fractional nonlinear Schrödinger equation

2014/12/04 by Torres, César, César Torres · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Fractional Differential Equations Solutions #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:26A33 #msc:34C37 #msc:35A15 #msc:35B38

paper · pdf · doi:10.48550/arxiv.1412.1674

arXiv admin note: text overlap with arXiv:1308.4215; and text overlap with arXiv:1208.2545 by other authors without attribution

arxiv created 2014/12/04 · arxiv updated 2014/12/05

Abstract

We study the existence of positive solution for the one dimensional Schrödinger equation with mixed Lioville-Weyl fractional derivatives _tD_∞^α(_-∞D_t^αu(t)) + V(t) u(t) = f(u(t)), t∈ ℝ
u∈ H^α(ℝ).Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument.

Citations

• Ground state solution for a class of differential equations with left and right fractional derivatives

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