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Solutions of second order iterative boundary value problems with nonhomogeneous boundary conditions

  • Eric R. Kaufmann EMAIL logo and Nickolai Kosmatov
Published/Copyright: June 9, 2025
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Abstract

We consider the existence and uniqueness of solutions to the second order iterative boundary value problem

u(t)=ft,u(t),u[2](t),atb

where u[2](t) = u(u(t)), with solutions satisfying one of the following boundary conditions u(a) = a, u(b) = b or u(a) = b, u(b) = a. The Schauder fixed point theorem is used to establish our results.

MSC 2010: 34B15; 34K10; 39B05

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Received: 2024-07-02
Accepted: 2024-12-27
Published Online: 2025-06-09
Published in Print: 2025-06-26

© 2025 Mathematical Institute Slovak Academy of Sciences

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