Research PaperNo Access

The regularity properties and blow-up of the solutions for nonlocal Schrödinger equations

Department of Industrial Engineering, Antalya Bilim University, Dosemealti 07190, Antalya, Turkey

Center of Analytical-Information Resources, Azerbaijan State Economic University, 194 M. Mukhtarov, Baku AZ1001, Azerbaijan

Physics and Technical Sciences, Western Caspian University, Baku AZ1001, Azerbaijan

E-mail Address: veli.sahmurov@antalya.edu.tr

E-mail Address: veli.sahmurov@gmail.com

Corresponding author.

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and

Rishad Shahmurov

https://orcid.org/0000-0003-0644-5310

University of Alabama, Tuscaloosa, AL 35487, USA

E-mail Address: shahmurov@hotmail.com

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https://doi.org/10.1142/S0129055X24500302Cited by:0 (Source: Crossref)

Abstract

In this paper, the Cauchy problem for convolution-type nonlocal linear and nonlinear Schrödinger equations (NSEs) is studied. The equations include the general differential operators. The existence, uniqueness, $L^{p}$ -regularity properties of linear problem and the existence, uniqueness, and blow-up at finite time of the nonlinear problem are obtained. By choosing differential operators including in equations, the regularity properties of a different type of nonlocal Schrödinger equation are studied.

Keywords:

AMSC: 35Q55, 35Axx, 35Bxx, 35A05, 35B30

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