论文标题
有界域中具有亚自然生长项的准椭圆方程
Quasilinear elliptic equations with sub-natural growth terms in bounded domains
论文作者
论文摘要
我们考虑到类型\ [\ [\ begin {case} - δ_{ <q <p -1 $，其中$ω$是$ \ mathbb {r}^{n} $，$δ_{p，w} $中的一个有界域，是一个加权$ p $ -laplacian，而$σ$是$ω$的$ p $ -laplacian。我们为存在问题提供标准。为了证明，我们研究了$ p $ superharmonic功能的各种属性，尤其是无限度量数据的Dirichlet问题的解决性。
We consider the existence of positive solutions to weighted quasilinear elliptic differential equations of the type \[ \begin{cases} - Δ_{p, w} u = σu^{q} & \text{in $Ω$}, \\ u = 0 & \text{on $\partial Ω$} \end{cases} \] in the sub-natural growth case $0 < q < p - 1$, where $Ω$ is a bounded domain in $\mathbb{R}^{n}$, $Δ_{p, w}$ is a weighted $p$-Laplacian, and $σ$ is a nonnegative (locally finite) Radon measure on $Ω$. We give criteria for the existence problem. For the proof, we investigate various properties of $p$-superharmonic functions, especially the solvability of Dirichlet problems with infinite measure data.
