2020•MathematicsOpen access

Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments

Sebastián Buedo‐Fernández, Daniel Cao Labora, Rosana Rodríguez‐López, Stepan Agop Tersian

Abstract

We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear periodic boundary value problems associated with second-order differential equations with a functional dependence, which is a piecewise constant function. Our analysis lies in the study of the sign of the Green’s function.

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Key concepts: Sign (mathematics), Constant (computer programming), Piecewise, Mathematics, Boundary value problem, Constant function, Mathematical analysis, Function (biology)