NONCANONICAL THIRD-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH MIXED ARGUMENTS: OSCILLATION VIA CANONICAL TRANSFORM

Abstract The authors investigate the oscillatory and asymptotic behavior of solutions to the third-order nonlinear differential equation of noncanonical type with mixed deviating arguments $$\begin{aligned} (p_2(t)(p_1(t)y'(t))')'= q_1(t)y^{\mu }(\sigma (t))+q_2(t)y^{\lambda }(\tau (t)),\;t\ge t_0. \end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>p</mml:mi>