On the Behavior of Solutions of a Third-Order Nonlinear Dynamic Equation on Time Scales - Şenel, M. T. (Ukrains’kyi Matematychnyi Zhurnal, 2013)
We study oscillatory and asymptotic properties of the third-order nonlinear dynamic equation [ ( 1r_2(t) ( ( 1r_1(t) x^(t) ) ^γ_1 ) ^ ) ^γ_2 ]^+f( t,x^σ (t) )=0,tT. By using the Riccati transformation, we present new criteria for the oscillation or certain asymptotic behavior of solutions of this equation. It is supposed that the time scale T is unbounded above.