Neutral differential equations are studied. Sufficient conditions are obtained to have oscillatory solutions or nonoscillatory solutions. For the existence of solutions, the Schauder-Tikhonov fixed point theorem is used.
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Certain hyperbolic equations with continuous distributed deviating arguments are studied, and sufficient conditions are obtained for every solution of some boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems for functional differential inequalities by using some integral means of solutions.
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