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.

在本文中，我们感兴趣的是研究狄利克雷分数 ( p ,  q )-拉普拉斯算子的一​​类奇异椭圆特征值问题解的多重性、唯一性和不存在性。所考虑的非线性涉及超临界索博列夫增长。我们的方法与子解法和超解法一起是变分的，通过这种方式，我们可以解决文献中尚未包含的广泛问题。即使\(W^{s_1,p}_0(\Omega ) \hookrightarrow L^{\infty }\left( \Omega \right) \)失败，我们也建立\(\Vert u\Vert _{L^{ \infty }\left( \Omega \right) } \le C[u]_{s_1,p}\)（对于某些\(C>0\)），当u是解时。