Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms
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Date
2018-06-18
Authors
Ji, Chao
Fang, Fei
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article we study the perturbed fractional Schrödinger equation involving oscillatory terms
(-∆)αu + u = Q(x) (ƒ(u) + ɛg(u)), x ∈ ℝN
u ≥ 0,
where α ∈ (0, 1) and N > 2α, (-∆)α stands for the fractional Laplacian, Q : ℝN → ℝN is a radial, positive potential, ƒ ∈ C([0, ∞), ℝ) oscillates near the origin or at infinity and g ∈ C([0, ∞), ℝ) with g(0) = 0. By using the variational method and the principle of symmetric criticality for non-smooth Szulkin-type functionals, we establish that: (1) the unperturbed problem, i.e. with ε = 0 has infinitely many solutions; (2) the number of distinct solutions becomes greater and greater when |ε| is smaller and smaller. Moreover, various properties of the solutions are also described in terms of the L∞- and Hα (ℝN)-norms.
Description
Keywords
Fractional Schrödinger equation, Multiple solutions, Oscillatory terms
Citation
Ji, C., & Fang, F. (2018). Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms. <i>Electronic Journal of Differential Equations, 2018</i>(126), pp. 1-21.
Rights
Attribution 4.0 International