We study existence of solutions for a boundary degenerate (or singular) quasilinear equation in a smooth bounded domain under Dirichlet boundary conditions. We consider a weighted $p$-Laplacian operator with a coefficient that is locally bounded inside the domain and satisfying certain additional integrability assumptions. Our main result applies for boundary value problems involving continuous non-linearities having no growth restriction, but provided the existence of a sub and a supersolution is guaranteed. As an application, we present an existence result for a boundary value problem with a non-linearity $f\left(u\right)$ satisfying $f\left(0\right)\le 0$ and having $(p-1)$-sublinear growth at infinity.

我们研究在Dirichlet边界条件下在光滑有界域中的边界退化（或奇异）拟线性方程解的存在性。我们考虑加权$p$-拉普拉斯算子，其系数在域内局部有界，并且满足某些其他可积性假设。我们的主要结果适用于涉及连续非线性且无增长限制的边值问题，但前提是存在子项和上解是有保证的。作为应用，我们给出了非线性非线性边值问题的存在结果$F（ü）$ 满意的 $F（0）\le 0$ 并有 $（p-\mathrm{1个}）$-在无限远处的亚线性增长。