Existence and Uniqueness of Solutions for a Class of Singular Nonlinear Two-Point Boundary Value Problems with Sign-Changing Nonlinear Terms. (4th March 2017)

• Record Type: Journal Article
• Authors: Dinmohammadi, Abdollah; Shivanian, Elyas; Razani, Abdolrahman
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 3(2017)
• Page Start: 344
• Page End: 359
• Publication Date: 2017-03-04
• Subjects: Constructive theorem -- existence and uniqueness -- sign-changing nonlinear terms -- singular boundary value problem; 34B15 -- 34B16 -- 34K10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1276073
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, a constructive proof under some conditions is presented for existence and uniqueness of the solutions to the singular problem with the boundary conditions In general, f ( x, y ( x )) is assumed to be nonsingular with respect to the independent variable x but it is allowed be singular with respect to y and moreover, f ( x, y ( x )) can be sign changing as well. The Picard iterative sequence is then constructed based on integral equation with the help of positive Green's function. The convergence of this iterative sequence is controlled by an adjustable parameter so that it converges to the unique solution in the finite region in which is supposed to be nonnegative and bounded. Some examples also are given to demonstrate the trustworthiness of our constructive theory.