Displaying similar documents to “A remark on power comparison theorem for half-linear differential equations”

Oscillatory properties of second order half-linear difference equations

Pavel Řehák (2001)

Czechoslovak Mathematical Journal

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We study oscillatory properties of the second order half-linear difference equation Δ ( r k | Δ y k | α - 2 Δ y k ) - p k | y k + 1 | α - 2 y k + 1 = 0 , α > 1 . ( HL ) It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation Δ ( r k Δ y k ) - p k y k + 1 = 0 . We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.

Global monotonicity and oscillation for second order differential equation

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini (2005)

Czechoslovak Mathematical Journal

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Oscillatory properties of the second order nonlinear equation ( r ( t ) x ' ) ' + q ( t ) f ( x ) = 0 are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.