RETRACTED ARTICLE:Existence of global solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation

Abstract

This paper is concerned with the global existence of solutions for the semilinear nonlocal fractional Cauchy problem of the Schrödinger equation. Firstly, based on the Schrödinger approximation technique and the theory of a family of potential wells, the authors obtain the invariant sets and vacuum isolating of global solutions including the critical case. Then, the global existence of solutions and the stability of equilibrium points are discussed. Finally, the global asymptotic stability of the unique positive equilibrium point of the system is proved by applying the Leray-Schauder alternative fixed point theorem.

Retraction Note: Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions

“…The Editors-in-Chief have retracted this article because the results of this article are invalid. The article also shows significant overlap with an article by Liu [1] that was simultaneously under consideration with another journal, and with previously published articles [2,3]. The authors have not responded to correspondence regarding this retraction.…”