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DOAJ Open Access 2025

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

Yun-Ho Kim In Hyoun Kim
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Abstrak

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.

Topik & Kata Kunci

Thermodynamics Mathematics Analysis

Penulis (2)

Y

Yun-Ho Kim

I

In Hyoun Kim

Format Sitasi

APA MLA BibTeX
Kim, Y., Kim, I.H. (2025). A Brézis–Oswald-Type Result for the Fractional (<i>r</i>, <i>q</i>)-Laplacian Problems and Its Application. https://doi.org/10.3390/fractalfract9070412

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Informasi Jurnal
Tahun Terbit
2025
Sumber Database
DOAJ
DOI
10.3390/fractalfract9070412
Akses
Open Access ✓