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Open AccessArticle

On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient

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Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2
Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1197; https://doi.org/10.3390/sym12071197
Received: 1 July 2020 / Revised: 15 July 2020 / Accepted: 18 July 2020 / Published: 20 July 2020
This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form i α t α ω ( t , z ) + a 1 ( t ) Δ ω ( t , z ) + i α a 2 ( t ) ω ( t , z ) = ξ | ω ( t , z ) | p , ( t , z ) ( 0 , ) × R N , where N 1 , ξ C \ { 0 } and p > 1 , under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and consider the combined effects of absorption and dispersion terms. Further, we discuss in details some special cases of coefficient functions a 1 , a 2 L l o c 1 ( [ 0 , ) , R ) , and provide two illustrative examples. View Full-Text
Keywords: fractional in time nonlinear Schrödinger equation; absorption coefficient; dispersion parameter; global solution fractional in time nonlinear Schrödinger equation; absorption coefficient; dispersion parameter; global solution
MDPI and ACS Style

Jleli, M.; Samet, B.; Vetro, C. On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient. Symmetry 2020, 12, 1197. https://doi.org/10.3390/sym12071197

AMA Style

Jleli M, Samet B, Vetro C. On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient. Symmetry. 2020; 12(7):1197. https://doi.org/10.3390/sym12071197

Chicago/Turabian Style

Jleli, Mohamed; Samet, Bessem; Vetro, Calogero. 2020. "On a Fractional in Time Nonlinear Schrödinger Equation with Dispersion Parameter and Absorption Coefficient" Symmetry 12, no. 7: 1197. https://doi.org/10.3390/sym12071197

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