Classical non-negative solutions for one-dimensional Vlasov equation

A. Boukarou^a, S. G. Georgiev^b, K. Bouhali^c, Kh. Zennir<sup>c

a</sup> University of Science and Technology Houari Boumediene, Bab Ezzouar, 16000 Algeria
^b Sorbonne University, Paris, 75005 France
^c Qassim University, Buraydah, 51452 Saudi Arabia

Abstract: New fixed point approach based on certain topological properties is applied on the Vlasov equation to find classical non-negative solutions. This approach allows finding at least one solution and at least two solutions. It is shown how to apply this approach to the problem of finding classical non-negative solutions of the Vlasov equation.

Keywords: Vlasov equation, existence of solutions, iterative method, classical solution.

UDC: 517

Received: 09.07.2024
Revised: 20.08.2024
Accepted: 26.09.2024

DOI: 10.26907/0021-3446-2025-10-50-63