Work

A Note on a Min–Max Method for a Singular Kirchhoff Problem of Fractional Type

Year: 2024

Type: article

Abstract: In the present work, we study a fractional elliptic Kirchhoff-type problem that has a singular term. More precisely, we start by proving some properties related to the energy functional associated with the studied problem. Then, we use the variational method combined with the min–max method to prove that the energy functional reaches its global minimum. Finally, since the energy functional has a singularity, we use the implicit function theorem to show that the point where the minimum is reached is a weak solution for the main problem. To illustrate our main result, we give an example at the end of this paper.

Source: Mathematics

DOI: 10.3390/math12203269

Author: Ramzi Alsaedi

Institution: King Abdulaziz University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: King Abdulaziz University