Next Article in Journal
Generalized-Fractional Tikhonov-Type Method for the Cauchy Problem of Elliptic Equation
Previous Article in Journal
Slant Curves in Contact Lorentzian Manifolds with CR Structures
Open AccessArticle

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

School of Science, China University of Mining and Technology, Beijing 100083, China
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 47; https://doi.org/10.3390/math8010047
Received: 30 November 2019 / Revised: 24 December 2019 / Accepted: 26 December 2019 / Published: 1 January 2020
(This article belongs to the Section Difference and Differential Equations)
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. View Full-Text
Keywords: Lyapunov-type inequality; mixed Riemann–Liouville integral; mixed Caputo derivative; Green’s function; boundary value problem Lyapunov-type inequality; mixed Riemann–Liouville integral; mixed Caputo derivative; Green’s function; boundary value problem
MDPI and ACS Style

Wang, J.; Zhang, S. A Lyapunov-Type Inequality for Partial Differential Equation Involving the Mixed Caputo Derivative. Mathematics 2020, 8, 47.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop