In this work we are interested in the periodic solutions of the singular problem involving variable exponent with a homogeneous Dirichlet boundary conditions modeled as

Where \(\varOmega \) is an open regular bounded subset of \({\mathbb {R}}^{N}\), \(T>0\) is the period, \(\gamma (t,x)\) is a nonnegative periodic function belonging in \({\mathcal {C}}(\overline{Q_{T}})\) and f is a nonnegative measurable function periodic in time with period T and belonging to a certain Lebesgue space. Under suitable assumptions on \(\gamma \) and f, we prove an existence result of a nonnegative weak time periodic solution to the considered problem.

在这项工作中，我们对涉及变量指数的奇异问题的周期解感兴趣，其中齐次狄利克雷边界条件建模为

其中\(\varOmega \)是\({\mathbb {R}}^{N}\)的开正则有界子集，\(T>0\)是周期，\(\gamma (t,x) \)是属于\({\mathcal {C}}(\overline{Q_{T}})\)的非负周期函数，f是周期为T且属于某个勒贝格空间的非负可测函数. 在对\(\gamma \)和f 的适当假设下，我们证明了所考虑问题的非负弱时间周期解的存在性结果。