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

Ramzi Alsaedi ()
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Ramzi Alsaedi: Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2024, vol. 12, issue 20, 1-11

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.

Keywords: variational methods; singular equations; existence of solutions; min–max method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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