论文标题
各向异性的准线性问题的存在结果
An existence result for anisotropic quasilinear problems
论文作者
论文摘要
我们研究了在迪金莱特边界条件下平滑界面域中边界变性（或单数）准线性方程的解决方案的存在。我们考虑一个加权$ p-$ {l} aplacian运算符，其系数为{本地界限域内，并满足某些附加的集成性假设}。我们的主要结果适用于涉及没有生长限制的连续非线性性的边界价值问题，但前提是保证了子的存在并保证了超级分解。作为一个应用程序，我们为边界价值pro \ - blem提供了一个非线性$ f（u）$满足$ f（0）\ leq 0 $，具有$（p-1）-$ sublinear增长的存在结果。
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.
