This work explores the following singular-anisotropic boundary value problem 0.1 \(\begin{aligned} \left\{ \begin{array}{ll}-\displaystyle \sum \limits _{j\in \mathcal {E}} \partial _{j}\bigg [\frac{\vert \partial _{j}u\vert ^{p_{j}-2}\partial _{j}u}{(1+u)^{\theta }}\bigg ]+ \vert u\vert ^{s-1} u=\frac{f}{u^{\gamma }} & \hbox {in}\;\;\mathcal {D}, \\ u =0 & \hbox {on}\;\; \partial \mathcal {D}, \end{array} \right. \end{aligned}\) where \(\mathcal {D}\) is a bounded open domain in \(\mathbb {R}^{N}\) , \(\mathcal {E} = \{ j \in \mathbb {N} : 1 \le j \le N \}\) , and the parameters satisfy \(0< \gamma < 1\) , \(0 \le \theta \le 1\) , \(p_{j}>1\) for all \(j\in \mathcal {E}\) and \(f\in L^{m}(\mathcal {D})\) with \(m\ge 1\) . Our main goal is to show that the lower-order term \(\vert u\vert ^{s-1} u\) plays a key role in improving the regularity of solutions.
