Detecting nuanced and context-dependent offensive language remains a significant challenge for large language models (LLMs). While Parameter-Efficient Fine-Tuning (PEFT) methods like Low-Rank Adaptation (LoRA) offer an efficient way to adapt LLMs, their fixed-rank and dense update mechanisms can be suboptimal for capturing the subtle linguistic variations işaretleyici of offensiveness. In this paper, we propose Dynamic Sparse LoRA (DS-LoRA), a novel adaptive low-rank finetuning technique designed to enhance the identification of nuanced offensive language. DS-LoRA innovates by (1) incorporating input-dependent gating mechanisms that dynamically modulate the contribution of LoRA modules, and (2) promoting sparsity within the LoRA update matrices themselves through L1 regularization. This dual approach allows the model to selectively activate and refine only the most relevant parameters for a given input, leading to a more parsimonious and targeted adaptation. Extensive experiments on benchmark datasets demonstrate that DS-LoRA significantly outperforms standard LoRA and other strong baselines, particularly in identifying subtle and contextually ambiguous offensive content.