On the absence of global weak solutions for a nonlinear time-fractional Schrödinger equation

• Published in: Applicable analysis Vol. 103; no. 1; pp. 1 - 15
• Main Authors: Alotaibi, Munirah, Jleli, Mohamed, Ragusa, Maria Alessandra, Samet, Bessem
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.01.2024; Taylor & Francis Ltd
• Subjects: Boundary value problems; global weak solution; nonexistence; Nonlinear time-fractional Schrödinger equation; Schrodinger equation; singular logarithmic potential
• ISSN: 0003-6811; 1563-504X
• DOI: 10.1080/00036811.2022.2036335

In this paper, an initial value problem for a nonlinear time-fractional Schrödinger equation with a singular logarithmic potential term is investigated. The considered problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Using the test function method with a judicious choice of the test function, we obtain sufficient criteria for the absence of global weak solutions.