An existence result for anisotropic quasilinear problems

Abstract: 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.