Oscillatory Behavior of Second Oscillatory behavior of second order integro-dynamic equations with maxima and superlinear or sublinear neutral termsIntegro-Dynamic Equations With Maxima and Superlinear or Sublinear Neutral Terms
In this work, we present some new criteria for the oscillatory and the asymptotic behavior of the solutions of the following second-order mixed nonlinear integro-dynamic equations with maxima and superlinear or sublinear neutral terms on time scales equation* (r(t)(z^Δ(t))^γ)^Δ+_0^ta(t,s)f( s, x(s))Δ s+_i=1^nq_i(t) _s[τ_i(t), ξ_i(t)]x^α(s)=0, equation* where equation* z(t)=x(t)+p_1(t)x^λ_1 (η_1(t))+p_2(t)x^λ_2 (η_2(t)), t [0,+∞)_T. equation* The obtained results are new for both the discrete and continuous cases. Furthermore, our results extend known ones in the literature. An example is presented to illustrate the relevance of the results. , number=2, journal=Sarajevo Journal of Mathematics, author=Agwa, H. A. and Arafa, H. M. and Chatzarakis, G. E. and Naby, M. A. A., year=2022, month=Mar., pages=207–226