Nonexistence of global solutions for fractional temporal Schrödinger equations and systems
| dc.contributor.author | Azman, Ibtehal | |
| dc.contributor.author | Jleli, Mohamed | |
| dc.contributor.author | Kirane, Mokhtar | |
| dc.contributor.author | Samet, Bessem | |
| dc.date.accessioned | 2022-08-19T17:46:55Z | |
| dc.date.available | 2022-08-19T17:46:55Z | |
| dc.date.issued | 2017-11-08 | |
| dc.description.abstract | We, first, consider the nonlinear Schrödinger equation iαC0 Dαtu + ∆u = λ|u|p + μα(x) ‧ ∇|u|q, t > 0, x ∈ ℝN, where 0 < α < 1, iα is the principal value of iα, C0 Dαt is the Caputo fractional derivative of order α, λ ∈ ℂ\ {0}, μ ∈ ℂ, p > q > 1, u(t, x) is a complex-valued function, and α : ℝN → ℝN is a given vector function. We provide sufficient conditions for the nonexistence of global weak solution under suitable initial data. Next, we extend our study to the system of nonlinear coupled equations iαC0 Dαtu + ∆u = λ|v|p> + μα(x) ‧ ∇|v|q, t > 0, x ∈ ℝN, iβC0 Dβtv + ∆v = λ|u|k + μb(x) ‧ ∇|u|σ, t > 0, x ∈ ℝN, where 0 < β ≤ α < 1, λ ∈ ℂ\{0}, μ ∈ ℂ, p > q > 1, k > σ > 1, and α, b : ℝN → ℝN are two given vector functions. Our approach is based on the test function method. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Azman, I., Jleli, M., Kirane, M., & Samet, B. (2017). Nonexistence of global solutions for fractional temporal Schrödinger equations and systems. Electronic Journal of Differential Equations, 2017(276), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16077 | |
| 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, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional temporal Schrödinger equation | |
| dc.subject | Nonexistence | |
| dc.subject | Global weak solution | |
| dc.title | Nonexistence of global solutions for fractional temporal Schrödinger equations and systems | |
| dc.type | Article |