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Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations
Journal of Inequalities and Applications volume 2006, Article number: 42120 (2006)
We are concerned with the oscillatory and nonoscillatory behavior of solutions of even-order quasilinear functional differential equations of the type, where and are positive constants, and are positive continuous functions on, and is a continuously differentiable function such that,. We first give criteria for the existence of nonoscillatory solutions with specific asymptotic behavior, and then derive conditions (sufficient as well as necessary and sufficient) for all solutions to be oscillatory by comparing the above equation with the related differential equation without deviating argument.
Kiguradze IT: On the oscillatory character of solutions of the equation. Matematicheskii Sbornik. New Series 1964, 65 (107): 172–187.
Kusano T, Lalli BS: On oscillation of half-linear functional-differential equations with deviating arguments. Hiroshima Mathematical Journal 1994,24(3):549–563.
Kusano T, Naito M: Comparison theorems for functional-differential equations with deviating arguments. Journal of the Mathematical Society of Japan 1981,33(3):509–532. 10.2969/jmsj/03330509
Kusano T, Wang J: Oscillation properties of half-linear functional-differential equations of the second order. Hiroshima Mathematical Journal 1995,25(2):371–385.
Mahfoud WE: Comparison theorems for delay differential equations. Pacific Journal of Mathematics 1979,83(1):187–197.
Tanigawa T: Oscillation and nonoscillation theorems for a class of fourth order quasilinear functional differential equations. Hiroshima Mathematical Journal 2003,33(3):297–316.
Tanigawa T: Oscillation criteria for a class of higher order nonlinear differential equations. Memoirs on Differential Equations and Mathematical Physics 2006, 37: 137–152.
Tanigawa T, Fentao W: On the existence of positive solutions for a class of even order quasilinear differential equations. Advances in Mathematical Sciences and Applications 2004,14(1):75–85.
Wang J: Oscillation and nonoscillation theorems for a class of second order quasilinear functional-differential equations. Hiroshima Mathematical Journal 1997,27(3):449–466.
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Manojlović, J., Tanigawa, T. Oscillation and nonoscillation theorems for a class of even-order quasilinear functional differential equations. J Inequal Appl 2006, 42120 (2006). https://doi.org/10.1155/JIA/2006/42120
- Differential Equation
- Continuous Function
- Positive Constant
- Asymptotic Behavior
- Differentiable Function