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1. chinaXiv:201805.00171 [pdf]

Lyapunov-type inequalities for ψ?Laplacian equations

Zheng, Jun; Guo, Xu
Subjects: Mathematics >> Mathematics (General)

In this work, we present several Lyapunov-type inequalities for a class of $\psi-$Laplacian equations of the form \begin{align*} (\psi(u'(x)))'+r(x)f(u(x))=0, \end{align*} with Dirichlet boundary conditions, where $\psi$ and $f$ satisfies certain structural conditions with general nonlinearities. We do not require any sub-multiplicative property of $\psi$, and any convexity of $\frac{1}{\psi(t)}$ or $\psi (t)t$ in the establishment of Lyapunov-type inequalities. The obtained inequalities can be seen as extensions and complements of the existing results in the literature.

submitted time 2018-05-22 Hits8397Downloads987 Comment 0

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