Nonexistence of Solutions of Higher-order Nonlinear Non-gauge Schrödinger Equation

Ahmed Alsaedi; Bashir Ahmad; Mokhtar Kirane; Abderrazak Nabti

doi:10.5269/bspm.47911

Nonexistence of Solutions of Higher-order Nonlinear Non-gauge Schrödinger Equation

Ahmed Alsaedi, Bashir Ahmad, Mokhtar Kirane, Abderrazak Nabti

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A nonexistence result is proved of the space higher-order nonlinear Schrödinger equation (equation presented) where m > 1, n > 1 and p > n. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 × 2 - system (equation presented) where m > 1, p, q > 1, and λ, δ ∈ C\{0}.

Original language	British English
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	40
DOIs	https://doi.org/10.5269/bspm.47911
State	Published - 2022

Keywords

Local and global existence
Nonexistence of solutions
Schrödinger equation

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10.5269/bspm.47911

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title = "Nonexistence of Solutions of Higher-order Nonlinear Non-gauge Schr{\"o}dinger Equation",

abstract = "A nonexistence result is proved of the space higher-order nonlinear Schr{\"o}dinger equation (equation presented) where m > 1, n > 1 and p > n. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 × 2 - system (equation presented) where m > 1, p, q > 1, and λ, δ ∈ C\{0}.",

keywords = "Local and global existence, Nonexistence of solutions, Schr{\"o}dinger equation",

author = "Ahmed Alsaedi and Bashir Ahmad and Mokhtar Kirane and Abderrazak Nabti",

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doi = "10.5269/bspm.47911",

language = "British English",

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journal = "Boletim da Sociedade Paranaense de Matematica",

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T1 - Nonexistence of Solutions of Higher-order Nonlinear Non-gauge Schrödinger Equation

AU - Alsaedi, Ahmed

AU - Ahmad, Bashir

AU - Kirane, Mokhtar

AU - Nabti, Abderrazak

PY - 2022

Y1 - 2022

N2 - A nonexistence result is proved of the space higher-order nonlinear Schrödinger equation (equation presented) where m > 1, n > 1 and p > n. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 × 2 - system (equation presented) where m > 1, p, q > 1, and λ, δ ∈ C\{0}.

AB - A nonexistence result is proved of the space higher-order nonlinear Schrödinger equation (equation presented) where m > 1, n > 1 and p > n. Our method of proof rests on a judicious choice of the test function in the weak formulation of the equation. Then, we obtain an upper bound of the life span of solutions. Furthermore, the necessary conditions for the existence of local or global solutions are provided. Next, we extend our results to the 2 × 2 - system (equation presented) where m > 1, p, q > 1, and λ, δ ∈ C\{0}.

KW - Local and global existence

KW - Nonexistence of solutions

KW - Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85124143280&partnerID=8YFLogxK

U2 - 10.5269/bspm.47911

DO - 10.5269/bspm.47911

M3 - Article

AN - SCOPUS:85124143280

SN - 0037-8712

VL - 40

JO - Boletim da Sociedade Paranaense de Matematica

JF - Boletim da Sociedade Paranaense de Matematica

ER -

Nonexistence of Solutions of Higher-order Nonlinear Non-gauge Schrödinger Equation

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Keywords

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