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arXiv · 2306.13603

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

A. L. A. de Araujo·Aldo H. S. Medeiros
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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 $W^{s_1,p}_0(\Omega) \hookrightarrow L^{\infty}\left(\Omega\right)$ failing, we establish $\|u\|_{L^{\infty}\left(\Omega\right)} \leq C[u]_{s_1,p}$ (for some $C>0$ ), when $u$ is a solution.

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A. L. A. de Araujo, Aldo H. S. Medeiros. 2023-06-23. Eigenvalue for a problem involving the fractional (p,q)-Laplacian operator and nonlinearity with a singular and a supercritical Sobolev growth. https://arxiv.org/abs/2306.13603

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