Solvability of a Second Order Boundary Value Problem.
Nacira Hamidane1*, Assia Guezane-Lakoud2
1Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar –Annaba-University , Annaba, Algeria
2Laboratory of Advanced Materials, Faculty of Sciences, Badji Mokhtar –Annaba-University , Annaba, Algeria
* Corresponding author: nhamidane@yahoo.com
Presented at the Ist International Symposium on Innovative Approaches in Scientific Studies (ISAS 2018), Kemer-Antalya, Turkey, Apr 11, 2018
SETSCI Conference Proceedings, 2018, 2, Page (s): 201-201 , https://doi.org/
Published Date: 23 June 2018 |
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Abstract
The study of nonlinear boundary value problems is a very important and difficult area of research in differential equations. The aim of our work is to establish the existence of solutions for a second order boundary value problem which models different real situations especially in physics and mechanics. Our approach consists to modify the given problem and prove the existence results of the modified one which are equivalent, using fixed point theory combined with the lower and upper solutions method. We need also to introduce the Nagumo condition to get bounds of the first derivative because the term of nonlinearity depends on it.
Keywords - Boundary value problem. Existence of solutions. Fixed point theorem
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