Existence and uniqueness theorems of second-order equations with integral boundary conditions
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 899-911
https://doi.org/10.4134/BKMS.b170374
Published online May 31, 2018
Lazhar Bougoffa, Ammar Khanfer
Al Imam Mohammad Ibn Saud Islamic University, Al Imam Mohammad Ibn Saud Islamic University
Abstract : In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions $\mu$ and $h_{i}$, $i=1,2$ that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).
Keywords : second-order equation, nonlocal boundary conditions, existence and uniqueness solution, Adomian decomposition method
MSC numbers : Primary 34B10
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