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In this work, we consider the existence of nonoscillatory solutions of second order nonlinear neutral differential equations. Our results include as special cases some well-known results for linear and nonlinear equations. We use the Lebesgue’s dominated convergence theorem and Banach contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.

Existence of nonoscillatory solutions for second-order nonlinear differential equations of neutral type