Abstract
We consider the nonoscillatory half-linear differential equation ( r ( t ) Φ ( x ′ ) ) ′ + c ( t ) Φ ( x ) = 0 , Φ ( x ) ≔ | x | p − 2 x , p > 1 , and we study oscillatory properties of its perturbation (∗ ) [ ( r ( t ) + r ̃ ( t ) ) Φ ( x ′ ) ] ′ + ( c ( t ) + c ̃ ( t ) ) Φ ( x ) = 0 . We use the Riccati technique and relationship between (∗) and a certain associated linear equation. The results are applied to the perturbed Euler-type equation.
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