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Leighton-Hille-Kneser-type oscillation criteria for Emden-Fowler neutral delay differential equations
AIMS Mathematics 2025, 10(12): 29873-29891
Published: 18 December 2025
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Emden-Fowler differential equations have numerous applications in physics and engineering. In this article, we extended the classical Leighton, Hille, and Kneser types oscillation criteria for second-order linear differential equations to the second-order Emden-Fowler neutral delay differential equation

( r ( t ) | z ( t ) | α 1 z ( t ) ) + q ( t ) | y ( σ ( t ) ) | β sgn y ( σ ( t ) ) = 0 , t t 0 ,

where z ( t ) = y ( t ) + p ( t ) y ( τ ( t ) ) . The criteria obtained extended and improved some well-known results reported in the literature. Moreover, several examples are provided to show the significance of the new findings.

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