Abstract
In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problems for the Dirichlet fractional (p, q)-Laplacian. The nonlinearity considered involves supercritical Sobolev growth. Our approach is variational together with the sub- and supersolution methods, and in this way we can address a wide range of problems not yet contained in the literature. Even when \(W^{s_1,p}_0(\Omega ) \hookrightarrow L^{\infty }\left( \Omega \right) \) failing, we establish \(\Vert u\Vert _{L^{\infty }\left( \Omega \right) } \le C[u]_{s_1,p}\) (for some \(C>0\) ), when u is a solution.
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The first author was partially supported by FAPEMIG/ APQ-02375-21, FAPEMIG/RED00133-21, and CNPq Processes 101896/2022-0, 305447/2022-0.
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All the authors take part in the project projeto Special Visiting Researcher - FAPEMIG CEX APQ 04528/22.
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de Araujo, A.L.A., Medeiros, A.H.S. Eigenvalue for a problem involving the fractional (p, q)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth. Anal.Math.Phys. 14, 16 (2024). https://doi.org/10.1007/s13324-024-00873-7
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DOI: https://doi.org/10.1007/s13324-024-00873-7