In the present work, we prove an existence and uniqueness result of solutions to a quasilinear elliptic problem with nonlinear singular terms in the weighted Sobolev space. The equation that we consider is the following

$$\begin{aligned} -\Delta _{p(\cdot )}^{\omega } u+\beta (u)=\frac{f(x)}{u^{\alpha }}, \end{aligned}$$

where \(\alpha \ge 1\), \(\beta \) is a continuous non decreasing surjective real function on \({\mathbb {R}}\), f is a nonnegative function belonging to the Lebesgue space \(L^{m}(\Omega )\) and \(m\ge 1\).

中文翻译：

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加权$$ p（\ cdot）$$ p（·）-具有非线性奇异项的拉普拉斯问题

在目前的工作中，我们证明了在加权Sobolev空间中具有非线性奇异项的拟线性椭圆问题解的存在性和唯一性结果。我们考虑的等式如下

$$ \ begin {aligned}-\ Delta _ {p（\ cdot）} ^ {\ omega} u + \ beta（u）= \ frac {f（x）} {u ^ {\ alpha}}，\ end {已对齐} $$

其中\（\ alpha \ ge 1 \），\（\ beta \）是\（{\ mathbb {R}} \）上的连续非递减实数实函数，f是属于Lebesgue空间\（ L ^ {m}（\ Omega）\）和\（m \ ge 1 \）。