Existence and Uniqueness of Solutions for the System of First-order Nonlinear Differential Equations with Three-point and Integral Boundary Conditions
In the paper, the existence and uniqueness of the solutions for the system of the nonlinear first-order ordinary differential equations with three-point and integral boundary conditions are studied. The Green function is constructed and the considered problem is reduced to the equivalent integral equation. The existence and uniqueness of the solutions for the given problem are analyzed by using the Banach contraction principle. The Schaeferâ€™s fixed point theorem is then
used to prove the existence of the solutions. Finally, the examples are given to verify the given theorems.
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