New criteria for oscillation of nonlinear neutral differential equations

By Osama Moaaz. 2019

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AbstractThe aim of this work is to offer sufficient conditions for the oscillation of neutral differential equation second order (r(t)[(y(t)+p(t)y(τ(t)))′]γ)′+f(t,y(σ(t)))=0,$$ \bigl( r ( t ) \bigl[ \bigl( y ( t ) +p ( t ) y \bigl( \tau ( t ) \bigr) \bigr) ^{\prime } \bigr] ^{\gamma } \bigr) ^{\prime }+f \bigl( t,y \bigl( \sigma ( t ) \bigr) \bigr) =0, $$ where ∫∞r−1/γ(s)ds=∞$\int ^{\infty }r^{-1/\gamma } ( s ) \,\mathrm{d}s= \infty $. Based on the comparison with first order delay equations and by employ the Riccati substitution technique, we improve and complement a number of well-known results. Some examples are provided to show the importance of these results.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8910918b611b92d0e91c86be4445bda3d1eee10b