论文标题
涉及奇异性及其应用的P拉普拉斯方程的强大比较原理
Strong comparison principle for a p-Laplace equation involving singularity and its applications
论文作者
论文摘要
在本文中，我们证明了一个强大的比较原理，用于径向减小解决方案$ u，v \ in C_ {0}^{1，α}（\ bar {b_r}）$-Δ_Pu- \ frac u- \ frac {1}} v- \ frac {1} {v^δ} = g（x）$ in $ b_r $。在这里，我们假设$ 1 <p <2，\; Δ\ in（0,1）$和$ f，g $是连续的，径向的功能，因此$ 0 \ leq f \ leq g $，但$ f \ not \ equiv g $ in $b_r。$ b_r。$ p> $ p> 2 $ $ p> 2 $ a在强大的比较原则的情况下提供了反例。作为强比较原理的应用，我们证明了P-Laplace方程的三个解决方案定理，并用一个示例说明。
In this paper we prove a strong comparison principle for radially decreasing solutions $u,v\in C_{0}^{1,α}(\Bar{B_R})$ of the singular equations $-Δ_p u-\frac{1}{u^δ}=f(x)$ and $-Δ_p v-\frac{1}{v^δ}=g(x)$ in $B_R$. Here we assume that $ 1<p<2 , \; δ\in (0,1)$ and $f,g$ are continuous, radial functions such that $0 \leq f \leq g$ but $f\not \equiv g$ in $B_R.$ For the case $p>2$ a counterexample is provided where the strong comparison principle is violated. As an application of strong comparison principle, we prove a three solution theorem for p-Laplace equation and illustrate with an example.
