A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application

A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application

This study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi>&...

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Bibliographic Details
Main Authors: Yun-Ho Kim, In Hyoun Kim
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Fractal and Fractional
Subjects:
fractional (<i>r</i>, <i>q</i>)-Laplacian
Kirchhoff-type function
uniqueness
global minima
Online Access:https://www.mdpi.com/2504-3110/9/7/412
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Summary:This study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator and discontinuous Kirchhoff-type coefficients. The Brézis–Oswald-type result and Ricceri’s abstract global minimum principle are critical tools in identifying this uniqueness. We consider an eigenvalue problem associated with fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian problems to confirm the existence of a positive solution for our problem without the Kirchhoff coefficient. Moreover, we establish the uniqueness result of the Brézis–Oswald type by exploiting a generalization of the discrete Picone inequality.
ISSN:2504-3110

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