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arXiv 2003.11186math.AP
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具多个次自然增长项的拟线性椭圆型方程极小解的存在性

Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms

Takanobu Hara, Adisak Seesanea

备注：
Published online in Nonlinear Analysis
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摘要：

研究了\[ -Δ_{p} u = σu^{q} + μ\quad \text{in} \ \mathbb{R}^{n}, \]型拟线性椭圆型方程在次自然增长情形$0 < q < p - 1$下正解的存在性，其中$Δ_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$是具有$1 < p < n$的$p$ -Laplacian，$σ$和$μ$是$\mathbb{R}^{n}$上的非负Radon测度.在一定的广义能量条件下，构造了$σ$和$μ$上的极小广义解.为了证明这一点，我们给新的估计措施之间的相互作用。我们还构造了几个亚自然增长项方程的解决方案，使用相同的方法。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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