Lyapunov-type inequalities for a class of nonlinear higher order differential equations

分类： 数学 >> 数学（综合） 提交时间： 2018-06-04

Jun Zheng Haofan Wang

摘要： In this work, we establish several Lyapunov-type inequalities for a class of nonlinear higher order differential equations having a form \begin{align*} (\psi(u^{(m)}(x)))'+\sum_{i=0}^nr_i(x)f_i(u^{(i)}(x))=0, %\ \ \ \ \text{or}\ \ \ \ (\psi(u^{(m)}))^{(m)}+r_i(x)f(u)=0, \end{align*} with anti-periodic boundary conditions, where $m> n\geq 0$ are integers, $\psi$ and $f_i (i=0,1,2,...,n)$ satisfy certain structural conditions such that the considered equations have general nonlinearities. The obtained inequalities are extensions and complements of the existing results in the literature.

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