The Existence of a Solution to a Class of Fractional Double Phase Problems
Abstrak
This paper focuses on the study of a class of fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>&</mo><mi>q</mi></mrow></semantics></math></inline-formula>-Laplacian problems with unbalanced growth, which includes vanishing potential and a supercritical growth exponent. By employing the mountain pass theorem alongside the Truncation method, penalization method, and Moser iteration method, the main result establishes the existence of a nontrivial solution under conditions of low perturbations of supercritical nonlinearity. Furthermore, we derive <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>L</mi><mo>∞</mo></msup><mrow><mo>(</mo><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> estimates and the interior Hölder regularity of weak solutions in the context of supercritical growth.
Topik & Kata Kunci
Penulis (2)
Maoji Ri
Yongkun Li
Akses Cepat
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- 2024
- Sumber Database
- DOAJ
- DOI
- 10.3390/fractalfract8110621
- Akses
- Open Access ✓