Oscillation of higher-order differential equations with distributed delay

Résumé

This paper deals with the oscillation properties of higher-order nonlinear differential equations with distributed delay $$ \bigl[ b ( \ell ) \bigl( y^{ ( n-1 ) } ( \ell ) \bigr) ^{\gamma} \bigr] ^{\prime}+ \int_{c}^{d}q ( \ell, \xi ) y^{\gamma} \bigl( g ( \ell, \xi ) \bigr) \,d ( \xi ) =0, \quad \ell\geq\ell_{0}, $$ under the condition $$ \int_{\ell_{0}}^{\infty}\frac{1}{b^{\frac{1}{\gamma}} ( \ell ) }\,d\ell< \infty. $$ We obtain new oscillation criteria by employing a refinement of the generalized Riccati transformations and new comparison principles. We provide some examples to illustrate the main results.

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