Title: Existence and multiplicity of solutions for the fractional Schrödinger equation with steep potential well and perturbation

Authors: Peiluan Li; Yuan Yuan

Addresses: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, 471023, Henan, China ' Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1B 3X7, Canada

Abstract: In the present paper, we investigate the solutions of a fractional Schrödinger equation with sublinear perturbation and steep potential well. First, we obtain the existence of at least one solution by the minimisation result due to Mawhin and Willem. Second, by virtue of the symmetric mountain pass theorem, the existence criteria of infinitely many solutions are established. Lastly, an example is given to demonstrate the main results.

Keywords: fractional Schrödinger equations; steep potential well; infinitely many solutions.

DOI: 10.1504/IJDSDE.2019.103733

International Journal of Dynamical Systems and Differential Equations, 2019 Vol.9 No.4, pp.335 - 348

Received: 18 Jan 2018
Accepted: 19 Apr 2018

Published online: 26 Nov 2019 *

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