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Research Article | Open Access

Existence, uniqueness, and localization of positive solutions to nonlocal problems of the Kirchhoff type via the global minimum principle of Ricceri

In Hyoun Kim1, Yun-Ho Kim2( )
Department of Mathematics, Incheon National University, Incheon 22012, Korea, Republic of Korea
Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea
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Abstract

The purpose of this paper is to demonstrate the existence and uniqueness of positive solutions to fractional p-Laplacian problems with discontinuous Kirchhoff-type functions. The crucial tools for getting these results are the uniqueness result of the Brézis–Oswald–type problem and the abstract global minimum principle. The primary features of this paper are the discontinuity of the Kirchhoff coefficient in [ 0 , ∞ ) and the localization of solutions.

Keywords

fractional p-LaplacianKirchhoff-type functionweak solutionuniquenessglobal minima
CLC number: 35B33, 35D30, 35J20, 35J60, 35J66

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 4540-4557
DOI: 10.3934/math.2025210

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Kim IH, Kim Y-H. Existence, uniqueness, and localization of positive solutions to nonlocal problems of the Kirchhoff type via the global minimum principle of Ricceri. AIMS Mathematics, 2025, 10(3): 4540-4557. https://doi.org/10.3934/math.2025210

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Received: 11 October 2024
Revised: 13 January 2025
Accepted: 27 January 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)