Interval oscillation criteria for second order mixed nonlinear forced impulsive differential equation with damping term (Q2913830)

The authors consider the second-order forced impulsive differential equations with mixed non-linearities of the form NEWLINE\[NEWLINE \begin{cases} (r(t)\Phi _\alpha (x'(t)))' + p(t)\Phi _\alpha ((x'(t)) + \Phi_\alpha (x(t)) + \sum_{i = 1}^n q_i (t)\Phi _{\beta _i } (x(t)) = e(t),\;t \neq \tau _k , \\ x(\tau _k^ + ) = a_k x(\tau _k ),\;x' (\tau_k^+) = b_k x' (\tau_k ),\;k = 1,2,\dots . \end{cases}NEWLINE\]NEWLINE The authors obtain certain interval conditions under which the second-order forced impulsive differential equations with mixed non-linearities of the above form are oscillatory. Some examples are given to illustrate the theoretical analysis made in this work.