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

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 3; pp. 4540 - 4557
Main Authors Kim, In Hyoun, Kim, Yun-Ho
Format Journal Article
LanguageEnglish
Published AIMS Press 01.03.2025
Subjects
fractional $ p $-laplacian
global minima
kirchhoff-type function
uniqueness
weak solution
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Summary: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, \infty) $ and the localization of solutions.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025210