Eigenvalue for a problem involving the fractional (p,q)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth

2023/06/23 by Anderson L. A. de Araújo, de Araujo, A. L. A., Aldo H. S. Medeiros +1
Computer Science · Mathematics · #35J75 35R11 35J67 35A15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2306.13603

openalex publication_date 2023/06/23 · openalex created_date 2023/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional (p,q)-Laplacian. The nonlinearity considered involves supercritical Sobolev growth. Our approach is variational togheter with the sub- and supesolution methods, and in this way we can address a wide range of problems not yet contained in the literature. Even when W^s₁,p₀(Ω) \hookrightarrow L^∞(Ω) failing, we establish ‖u‖_L^∞(Ω) ≤ C[u]_s1,p (for some C>0 ), when u is a solution.

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