On the existence of solutions of a class of singular nonlinear two-point boundary value problems

Existence theory for nonresonant singular boundary value problems

“…In Section 3 fixed point methods (in particular a nonlinear alternative of Leray-Schauder type) is used to obtain an existence principle. The final section establishes some existence results for (1.1); these results extend and complement the theory in [4,6,21].…”

A collection of computational techniques for solving singular boundary-value problems

“…New difference methods for computing the numerical values of u x and u y are also discussed. These approximations are found to yield O(h 4 ) accuracy, when used in conjunction with nine-point formula proposed by (Chawla and Shivkumar [7]) Remark 2. The central difference scheme and the upwind difference scheme are most commonly used to solve this type of problem.…”

“…In this paper author applies a monotone iterative method directly to the singular problems (2.1) and (2.2) to establish the existence-uniqueness of the problem. Also, p(x) = x a , a 2 [0, 1), x 2 (0, 1] has a unique solution provided by Chawla and Shivkumar [7].…”

“…Here, author has obtained a new fourth-order compact finite difference discretization strategy based on arithmetic average discretization (Chawla and Shivkumar [7]) for the solution of twodimensional singularly perturbed non-linear elliptic partial differential equations, is directly applicable to problems in polar coordinates. The new fourth-order compact discretization strategy results in solving tri-block diagonal systems.…”

Wavelet Galerkin method for solving nonlinear singular boundary value problems arising in physiology

“…Existence and uniqueness of solution for such problems have been established by several researchers [25,26]. The balance of this paper is organized as follows.…”