A Lyapunov-Type Inequality for Partial Differential Equation Involving the Mixed Caputo Derivative

被引：5

作者：

Wang, Jie ^{[1
]}

Zhang, Shuqin ^{[1
]}

机构：

[1] China Univ Min & Technol, Sch Sci, Beijing 100083, Peoples R China

来源：

MATHEMATICS | 2020年 / 8卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Lyapunov-type inequality; mixed Riemann-Liouville integral; mixed Caputo derivative; Green's function; boundary value problem;

D O I：

10.3390/math8010047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we derive a Lyapunov-type inequality for a partial differential equation on a rectangular domain with the mixed Caputo derivative subject to Dirichlet-type boundary conditions. The obtained inequality provides a necessary condition for the existence of nontrivial solutions to the considered problem and an example is given to illustrate it. Moreover, we present some applications to demonstrate the effectiveness of the new results.

引用

页数：11

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