Displaying similar documents to “Properties of solutions to a second order nonlinear differential equation.”

Oscillation conditions for first-order nonlinear advanced differential equations

Özkan Öcalan, Nurten Kiliç (2023)

Commentationes Mathematicae Universitatis Carolinae

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Our purpose is to analyze a first order nonlinear differential equation with advanced arguments. Then, some sufficient conditions for the oscillatory solutions of this equation are presented. Our results essentially improve two conditions in the paper “Oscillation tests for nonlinear differential equations with several nonmonotone advanced arguments” by N. Kilıç, Ö. Öcalan and U. M. Özkan. Also we give an example to illustrate our results.

Comparison theorems for noncanonical third order nonlinear differential equations

Ivan Mojsej, Ján Ohriska (2007)

Open Mathematics

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The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.