Oscillation Criteria of Second-Order Non-Linear Dynamic Equations with Integro Forcing Term on Time Scales

This paper is concerned with the oscillatory properties of second order non-linear dynamic equation with integro forcing term on an arbitrary time scales. We reduce our original dynamic equation into an alternate equation by introducing a function of forward jump operator. To study oscillations we establish some crucial Lemmas and employ generalized Riccati transformation technique which transforms our second order dynamic equation into the first order dynamic equation on an arbitrary time scales. These results also guarantee that the solution of our equation oscillates. Furthermore, we establish the Kamenev-type oscillation criteria of our system. At the end, we consider a second order dynamic equation on time scales with deviating argument and compare it with our result which gives the sufficient conditions of oscillation of it.

Keywords

time scale; dynamic equation; Riccati transformation technique; oscillation.

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