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Existence of positive solutions to a class of boundary value problems with derivative dependence on the half-line

  • Siham Ghiatou , John R. Graef EMAIL logo and Toufik Moussaoui
Published/Copyright: May 24, 2024
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Abstract

In this paper the authors prove the existence of a positive solution to the second order boundary value problem with a fully nonlinear term

u + λ u = a ( t ) f ( t , u ( t ) , u ( t ) ) , t I , u ( 0 ) = u = 0 ,

where I = (0, ∞), f : ℝ+ × ℝ+ × ℝ → ℝ+ and a : I → ℝ+ are continuous, and λ > 0. An example illustrates the main result.

Acknowledgement

The authors would like to thank the Referee for his/her valuable comments and suggestions for improvement.

  1. Communicated by Jozef Džurina

References

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Received: 2023-01-26
Accepted: 2023-08-06
Published Online: 2024-05-24
Published in Print: 2024-04-25

© 2024 Mathematical Institute Slovak Academy of Sciences

Downloaded on 25.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2024-0030/html
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