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Dinmohammadi, Abdollah; Shivanian, Elyas; Razani, Abdolrahman

Existence and uniqueness of solutions for a class of singular nonlinear two-point boundary value problems with sign-changing nonlinear terms. (English) Zbl 1372.34049

Numer. Funct. Anal. Optim. 38, No. 3, 344-359 (2017).
In this paper, the authors study existence and uniqueness of solutions for a class of singular nonlinear two-point boundary value problems with sign-changing nonlinear terms. They firstly give the Green’s function and its properties. Then, the Picard iterative sequence is constructed based on an integral equation and the positive Green’s function. They prove the Picard sequence can converge uniformly in a finite region so that it presents the unique solution to the boundary value problem. In addition, two examples are presented to illustrate their main results.
Reviewer: Hanying Feng (Shijiazhuang)

Cited in 7 Documents

MSC:

34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations

Keywords:

constructive theorem; existence and uniqueness; sign-changing nonlinear terms; singular boundary value problem; Picard sequence
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References:

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