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

Author

Listed:
  • Sebastián Buedo-Fernández

    (Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain)

  • Daniel Cao Labora

    (Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain)

  • Rosana Rodríguez-López

    (Instituto de Matemáticas e Departamento de Estatística, Análise Matemática e Optimización, Facultade de Matemáticas, Universidade de Santiago de Compostela, Campus Vida, 15782 Santiago de Compostela, Spain)

  • Stepan A. Tersian

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 8., 1113 Sofia, Bulgaria)

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.

Suggested Citation

  • Sebastián Buedo-Fernández & Daniel Cao Labora & Rosana Rodríguez-López & Stepan A. Tersian, 2020. "Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments," Mathematics, MDPI, vol. 8(11), pages 1-34, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1953-:d:439891
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