Journal of Mathematical Sciences

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> <…

Abstract This manuscript focuses on a suspension bridge system where the deck is modeled by the Timoshenko-Ehrenfest theory free of the second frequency spectrum. The existence and uniqueness of weak and strong solutions are proved by the Faedo-Galerkin method. The exponential decay is obtained without any restrictions on the coefficients of the system. The energy method is used for exponential s…