The existence of solutions and generalized Lyapunov-type inequalities to boundary value problems of differential equations of variable order

In this paper, we discuss the existence of solutions to a boundary value problem of differential equations of variable order, which is a piecewise constant function. Our results are based on the Schauder fixed point theorem. Then, under some assumptions on the nonlinear term, we obtain a generalized...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 4; pp. 2923 - 2943
Main Authors Zhang, Shuqin, Hu, Lei
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
derivatives and integrals of variable order
differential equations of variable order
existence
generalized lyapunov-type inequality
piecewise constant functions
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Summary:In this paper, we discuss the existence of solutions to a boundary value problem of differential equations of variable order, which is a piecewise constant function. Our results are based on the Schauder fixed point theorem. Then, under some assumptions on the nonlinear term, we obtain a generalized Lyapunov-type inequality to the two-point boundary value problem considered. To the best of our knowledge, there is no paper dealing with Lyapunov-type inequalities for boundary value problems in term of variable order. In addition, some examples of the obtained inequalities are given.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020189