In this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian

$$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$

with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

中文翻译：

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不同边界条件下二阶半线性差分方程的Sharp Lyapunov型不等式

在这项工作中，我们为具有p -Laplacian的二阶差分方程建立了最优 Lyapunov 型不等式

$$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\右| ^{p-2}u(k)=0 \end{对齐}$$

具有 Dirichlet、Neumann、混合、周期和反周期边界条件。