Geodesic
Oscillation results for second-order mixed neutral integro-dynamic equations with damping and a nonpositive neutral term on time scales
Novi Sad Journal of Mathematics, Tome 51 (2021) no. 2.

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In this work, we are concerned with studying a new class of second-order mixed neutral integro-dynamic equation with damping and a nonpositive neutral term of the form: \begin{equation}\label{h1} (r(t)(z^\Delta(t))^\gamma)^\Delta+ p(t)(z^\Delta(t))^\gamma+ g(t, x(\tau(t)))+\int\limits_{0}^{t}a(t,s)f( s, x(s))\Delta s=0, \end{equation} where \begin{equation}\label{h2} z(t)=x(t)-p_1(t)x(\eta_1(t))+p_2(t)x(\eta_2(t)), \end{equation} on a time scale $\mathbb{T}$. The obtained results not only present some new criteria for such kind of neutral differential equations and neutral difference equations as special cases, but also extend some results obtained on time scales. An example is given to illustrate the importance of our work.
Publié le :
DOI : 10.30755/NSJOM.12047
Classification : 34C10, 45D05, 34N05
Keywords: oscillation, time scales, integro-dynamic equations 
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     author = {H. A. Agwa and H. M. Arafa and G. E. Chatzarakis and M. A. Abdel Naby},
     title = {Oscillation results for second-order mixed neutral integro-dynamic equations with damping and a nonpositive neutral term on time scales},
     journal = {Novi Sad Journal of Mathematics},
     pages = {155 - 173},
     publisher = {mathdoc},
     volume = {51},
     number = {2},
     year = {2021},
     doi = {10.30755/NSJOM.12047},
     url = {http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12047/}
}
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H. A. Agwa; H. M. Arafa; G. E. Chatzarakis; M. A. Abdel Naby. Oscillation results for second-order mixed neutral integro-dynamic equations with damping and a nonpositive neutral term on time scales. Novi Sad Journal of Mathematics, Tome 51 (2021) no. 2. doi : 10.30755/NSJOM.12047. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.12047/

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