The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional \(p(\cdot )\)-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method can be implemented for an associated problem obtained by truncation related to the singularity. A comparison argument allows one to pass to the original singular problem.

中文翻译：

---

变阶非局部奇异方程的无穷多个大解

本文建立了一个非局部椭圆问题的无限多大能量解的存在，该问题涉及可变指数分数\(p(\cdot )\) -拉普拉斯算子和奇点，前提是问题中包含的正参数足够小。对于通过与奇异性相关的截断获得的关联问题，可以实施变分方法。比较参数允许人们传递到原始的奇异问题。