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

Abstract

We study the existence of positive solution for the one dimensional Schrödinger equation with mixed Lioville-Weyl fractional derivatives \begin{eqnarray*}\label{Eq00} _{t}D_{\infty}^α({_{-\infty}}D_{t}^αu(t)) + V(t) u(t) = & f(u(t)),\;\;t\in \mathbb{R}\\ u\in H^α(\mathbb{R}).\nonumber \end{eqnarray*} Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument.

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

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• Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

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