The existence of solutions and generalized Lyapunov-type inequalities to boundary value problems of differential equations of variable order
Shuqin Zhang, Lei Hu
Abstract
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.
Topics & Concepts
MathematicsBoundary value problemLyapunov functionPiecewiseVariable (mathematics)Mathematical analysisFree boundary problemFixed-point theoremApplied mathematicsNonlinear systemType (biology)EcologyBiologyQuantum mechanicsPhysicsNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations