论文标题
与不确定$ ϕ $ -laplacian类型方程相关的边界价值问题的积极解决方案的唯一性
Uniqueness of positive solutions for boundary value problems associated with indefinite $ϕ$-Laplacian type equations
论文作者
论文摘要
本文为诺伊曼的积极解决方案和与$ ϕ $ -DAPLACIAN方程相关的周期性边界价值问题提供了独特性结果$ a（t）$是逐步无限的重量，$ g（u）$是连续的功能。在处理$ p $ -laplacian差异操作员$ ϕ（s）= | s | |^{p-2} s $带有$ p> 1 $，以及nonlinear term $ g（u）= u^γ$ at \ mathbb {r} $，我们证明存在一个独特的积极解决方案，我们证明$γ\ in \ mathopen {]} - \ infty，（1-2p）/（p-1）\ mathclose {]} \ cup \ mathopen {]} p-1} p-1，++\ infty \ mathclose {[} $。
The paper provides a uniqueness result for positive solutions of the Neumann and periodic boundary value problems associated with the $ϕ$-Laplacian equation \begin{equation*} \bigl{(} ϕ(u') \bigr{)}' + a(t) g(u) = 0, \end{equation*} where $ϕ$ is a homeomorphism with $ϕ(0)=0$, $a(t)$ is a stepwise indefinite weight and $g(u)$ is a continuous function. When dealing with the $p$-Laplacian differential operator $ϕ(s)=|s|^{p-2}s$ with $p>1$, and the nonlinear term $g(u)=u^γ$ with $γ\in\mathbb{R}$, we prove the existence of a unique positive solution when $γ\in\mathopen{]}-\infty,(1-2p)/(p-1)\mathclose{]} \cup \mathopen{]}p-1,+\infty\mathclose{[}$.
