In this paper, we have obtained new sufficient conditions for oscillatory solutions of impulsive Euler-Bernoulli beam equations of the form \(\begin{aligned} \frac{\partial }{\partial t}\left( r\left( \frac{\partial w(x,t)}{\partial t}\right) \right) +q\frac{\partial w(x,t)}{\partial t}+p\frac{\partial ^4 w(x,t)}{\partial x^4}=f(x,t),\quad (x,t)\in G=(\varOmega \times \mathbb {R}{_+}), \end{aligned}\) \(\begin{aligned}w(x,t^+_k)=b_k(x,t_k,w), \end{aligned}\) \(\begin{aligned} w_t(x,t^+_k)=c_k(x,t_k,w_t), \quad k=1,2...,\ \ \\eUnALT \end{aligned}\) with clamped end boundary by using Riccati technique and integral average method. Our main goal is using the Jenson’s inequality to reduce the problem to ordinary differential inequality. We will establish sufficient conditions for the oscillation by the generalized Philo’s type. We provide several instances to demonstrate the usefulness of our recently derived results.

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Forced Oscillation of Certain Class of Impulsive Euler-Bernoulli Beam Equations with Damping Term

  • Sundaravadivel Priyadharshini,
  • Shyam Sundar Santra,
  • Vadivel Sadhasivam,
  • Debasish Majumder,
  • Prodipto Dhali

摘要

In this paper, we have obtained new sufficient conditions for oscillatory solutions of impulsive Euler-Bernoulli beam equations of the form \(\begin{aligned} \frac{\partial }{\partial t}\left( r\left( \frac{\partial w(x,t)}{\partial t}\right) \right) +q\frac{\partial w(x,t)}{\partial t}+p\frac{\partial ^4 w(x,t)}{\partial x^4}=f(x,t),\quad (x,t)\in G=(\varOmega \times \mathbb {R}{_+}), \end{aligned}\) \(\begin{aligned}w(x,t^+_k)=b_k(x,t_k,w), \end{aligned}\) \(\begin{aligned} w_t(x,t^+_k)=c_k(x,t_k,w_t), \quad k=1,2...,\ \ \\eUnALT \end{aligned}\) with clamped end boundary by using Riccati technique and integral average method. Our main goal is using the Jenson’s inequality to reduce the problem to ordinary differential inequality. We will establish sufficient conditions for the oscillation by the generalized Philo’s type. We provide several instances to demonstrate the usefulness of our recently derived results.