  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 $p-${L}aplacian 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 pro\-blem with a non-linearity
$f(u)$ satisfying $f(0) \leq 0$ and having $(p-1)-$sublinear growth at
infinity.
