论文标题
三阶非线性方程的lyapunov型不平等
Lyapunov-Type Inequalities for Third Order Nonlinear Equations
论文作者
论文摘要
我们得出了涉及多个$ψ$ -laplacian运算符的一般三阶非线性方程的lyapunov-type不等式的不等式， $ψ_{1} $是奇怪的，增加功能，$ψ_{2} $是超级物质的，$ψ_{1} $是次级的，并且$ \ frac {1} {ψ_{ψ_{1}} $是convex，并且$ f $是一个持续的功能，是一个持续的功能，可以满足sign sign sign sign sign sign sign sign sign。我们的结果利用$ q _ {+} $和$ q _ { - } $，而不是$ | q | $，它在文献中大多数结果中出现。此外，这些新的不平等现象概括了先前获得的结果，并且证明利用了与文献中大多数其他作品不同的技术。此外，使用所获得的不等式，我们对最大溶液的位置，振荡溶液的性质以及零的上限获得了限制。
We derive Lyapunov-type inequalities for general third order nonlinear equations involving multiple $ψ$-Laplacian operators of the form \begin{equation*} (ψ_{2}((ψ_{1}(u'))'))' + q(x)f(u) = 0, \end{equation*} where $ψ_{2}$ and $ψ_{1}$ are odd, increasing functions, $ψ_{2}$ is super-multiplicative, $ψ_{1}$ is sub-multiplicative, and $\frac{1}{ψ_{1}}$ is convex, and $f$ is a continuous function which satisfies a sign condition. Our results utilize $q_{+}$ and $q_{-}$, as opposed to $|q|$ which appears in most results in the literature. Additionally, these new inequalities generalize previously obtained results, and the proofs utilize a different technique than most other works in the literature. Furthermore, using the obtained inequalities, we obtain a constraint on the location of the maximum of a solution, properties of oscillatory solutions, and an upper bound for the number of zeroes.
