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Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

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  • Fei He

Abstract

We establish a fixed point theorem with w‐distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first‐order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

Suggested Citation

  • Fei He, 2014. "Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:309613
    DOI: 10.1155/2014/309613
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    References listed on IDEAS

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    1. Hamed H. Alsulami & Selma Gülyaz & Erdal Karapınar & İncı M. Erhan, 2014. "Fixed Point Theorems for a Class of α -Admissible Contractions and Applications to Boundary Value Problem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, July.
    2. Hamed H. Alsulami & Selma Gülyaz & Erdal Karapınar & İncı M. Erhan, 2014. "Fixed Point Theorems for a Class of α‐Admissible Contractions and Applications to Boundary Value Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    1. İncı M. Erhan, 2014. "Fixed Points of α‐Admissible Mappings on Partial Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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