一类带阻尼项的脉冲分数阶偏微分方程的强迫振动性

Forced oscillation of certain impulsive fractional partial differential equations with forcing term

  • 摘要: 考虑一类带阻尼项的非线性脉冲分数阶偏微分方程在Neumann边值条件下解的强迫振动性问题,首先利用积分平均方法,建立了该类方程所有解强迫振动的比较性定理,然后借助积分变换技巧和脉冲微分不等式方法,获得了该类方程所有解强迫振动的显式充分性判据,并提供一个例子来阐述主要结果的有效性和适用性.

     

    Abstract: We consider the forced oscillation problems for a kind of nonlinear impulsive fractional partial differential equations with forcing term under Neumann’s boundary value condition. First, we establish the comparison theorems for forced oscillation of solutions of such equations via integral averaging method, then we obtain the explicit sufficiency criteria for forced oscillation of solutions of such equations by employing integral transformation technique as well as impulsive differential inequality method, and finally we provide an example to illustrate the effectiveness and applicability of the main results.

     

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