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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).
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참고문헌 (23)
참고문헌 신청
G. Adomian / 1987 / Modification of the decomposition approach to the heat equation / J. Math. Anal. Appl. 124(1):290~291
G. Adomian / 1989 / Nonlinear Stochastic Systems Theory and Applications to Physics, Mathematics and its Applications, 46 / Kluwer Academic Publishers Group
G. Adomian / 1994 / Solving Frontier Problems of Physics: The Decomposition Method, Fundamental Theories of Physics, 60 / Kluwer Academic Publishers Group
L. Bougoffa / 2013 / Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the Adomian decomposition method / Appl. Math. Comput. 225:50~61
L. Bougoffa / 2011 / An approximate method for solving a class of weakly-singular Volterra integro-differential equations / Appl. Math. Comput. 217(22):8907~8913
G. Adomian / 1989 / Nonlinear Stochastic Systems Theory and Applications to Physics, Mathematics and its Applications, 46 / Kluwer Academic Publishers Group
G. Adomian / 1994 / Solving Frontier Problems of Physics: The Decomposition Method, Fundamental Theories of Physics, 60 / Kluwer Academic Publishers Group
L. Bougoffa / 2013 / Solving nonlocal initial-boundary value problems for linear and nonlinear parabolic and hyperbolic partial differential equations by the Adomian decomposition method / Appl. Math. Comput. 225:50~61
L. Bougoffa / 2011 / An approximate method for solving a class of weakly-singular Volterra integro-differential equations / Appl. Math. Comput. 217(22):8907~8913
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