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On the solvability of nonlinear first-order boundary-value problemsKeywords: Existence of solutions , boundary value problems , differential equations , fixed-point methods , differential inequalities. Abstract: This article investigates the existence of solutions to first-order nonlinear boundary-value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods.
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