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

Abstract

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.

Keywords:

• Nonlinear time-fractional Schrödinger equation
• singular logarithmic potential
• global weak solution
• nonexistence

2010 Mathematics Subject Classifications:

• 35B44
• 35B33
• 26A33

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The third author wish to thank Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Vietnam, for the opportunity to work in it. The second author is supported by Researchers Supporting Project number RSP2023R57, King Saud University, Riyadh, Saudi Arabia.