Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms
| dc.contributor.author | Ji, Chao | |
| dc.contributor.author | Fang, Fei | |
| dc.date.accessioned | 2022-02-14T19:37:31Z | |
| dc.date.available | 2022-02-14T19:37:31Z | |
| dc.date.issued | 2018-06-18 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 21 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15326 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Schrödinger equation | |
| dc.subject | Multiple solutions | |
| dc.subject | Oscillatory terms | |
| dc.title | Multiplicity of solutions for a perturbed fractional Schrödinger equation involving oscillatory terms | |
| dc.type | Article |