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Displaying similar documents to “On the oscillation of nonlinear differential systems with retarded arguments”

Non-oscillation of second order linear self-adjoint nonhomogeneous difference equations

N. Parhi (2011)

Mathematica Bohemica

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In the paper, conditions are obtained, in terms of coefficient functions, which are necessary as well as sufficient for non-oscillation/oscillation of all solutions of self-adjoint linear homogeneous equations of the form Δ ( p n - 1 Δ y n - 1 ) + q y n = 0 , n 1 , where q is a constant. Sufficient conditions, in terms of coefficient functions, are obtained for non-oscillation of all solutions of nonlinear non-homogeneous equations of the type Δ ( p n - 1 Δ y n - 1 ) + q n g ( y n ) = f n - 1 , n 1 , where, unlike earlier works, f n 0 or 0 (but ¬ 0 ) for large n . Further, these results are...

Oscillation of nonlinear differential systems with retarded arguments

Beatrix Bačová, Božena Dorociaková (2005)

Czechoslovak Mathematical Journal

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In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form y i ' ( t ) - p i ( t ) y i + 1 ( t ) = 0 , i = 1 , 2 , , n - 2 , y n - 1 ' ( t ) - p n - 1 ( t ) | y n ( h n ( t ) ) | α s g n [ y n ( h n ( t ) ) ] = 0 , y n ' ( t ) s g n [ y 1 ( h 1 ( t ) ) ] + p n ( t ) | y 1 ( h 1 ( t ) ) | β 0 , where n 3 is odd, α > 0 , β > 0 .