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Oscillation conditions for first-order nonlinear advanced differential equations

Özkan Öcalan, Nurten Kiliç (2023)

Commentationes Mathematicae Universitatis Carolinae

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.

Oscillation criteria for nonlinear differential equations with p ( t ) -Laplacian

Yutaka Shoukaku (2016)

Mathematica Bohemica

Recently there has been an increasing interest in studying p ( t ) -Laplacian equations, an example of which is given in the following form ( | u ' ( t ) | p ( t ) - 2 u ' ( t ) ) ' + c ( t ) | u ( t ) | q ( t ) - 2 u ( t ) = 0 , t > 0 . In particular, the first study of sufficient conditions for oscillatory solution of p ( t ) -Laplacian equations was made by Zhang (2007), but to our knowledge, there has not been a paper which gives the oscillatory conditions by utilizing Riccati inequality. Therefore, we establish sufficient conditions for oscillatory solution of nonlinear differential equations with...

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