论文标题
存在最小的溶液对具有多个亚自然生长项的准椭圆方程
Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms
论文作者
论文摘要
我们研究了类型\ [-Δ_{p} u =σu^{q} +μ\ quad \ text {in} \ \ \ \ \ \ \ \ m mathbb {r}^{n}，\ p <q <q <q p -1 $ n的存在阳性解决方案的存在。 \ cdot（| \ nabla u |^{p -2} \ nabla u）$是$ p $ -laplacian，$ 1 <p <n $，而$σ$和$μ$是$ \ mathbb {r}^{n} $。我们在$σ$和$μ$的某些广义能源条件下构建最小的广义解决方案。为了证明这一点，我们给出了措施之间相互作用的新估计。我们还使用相同的方法构建了具有多个亚自然生长项的方程解决方案。
We study the existence of positive solutions to quasilinear elliptic equations of the type \[ -Δ_{p} u = σu^{q} + μ\quad \text{in} \ \mathbb{R}^{n}, \] in the sub-natural growth case $0 < q < p - 1$, where $Δ_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$ is the $p$-Laplacian with $1 < p < n$, and $σ$ and $μ$ are nonnegative Radon measures on $\mathbb{R}^{n}$. We construct minimal generalized solutions under certain generalized energy conditions on $σ$ and $μ$. To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods.
