A Nonlocal Problem for a Second-Order Nonlinear Ordinary Differential Equation with Degeneration at the Boundary of the Domain

This paper investigates a nonlocal boundary value problem for a nonlinear second-order ordinary differential equation with degenerating coefficients at the boundaries of the interval. The differential equation is defined on the interval (0, 1) with degeneracy at both endpoints x = 0 and x = 1. The problem is reduced to an integral equation using the Green's function method. Under appropriate conditions on the nonlinear term, the existence and uniqueness of the solution are established based on the contraction mapping principle. Explicit estimates for the solution are provided using Gronwall's inequality.

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