Journal of East China Normal University(Natural Sc ›› 2013, Vol. 2013 ›› Issue (3): 149-163,175.

• Article • Previous Articles     Next Articles

Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions

LI Xi-liu1, MU Chun-lai1, ZENG Rong2, ZHOU Shou-ming1   

  1. 1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China;  2. School of Economic Mathematics, Southwestern
    University of Finance and Economics, Chengdu 611130, China
  • Received:2012-04-01 Revised:2012-07-01 Online:2013-05-25 Published:2013-07-10

Abstract: This paper considered the global non-existence of solutions
of nonlinear $p(x)$-Kirchhoff systems with dynamic boundary
conditions, which involve nonlinear external damping terms $Q$ and
nonlinear driving forces $f$. Through the study of the natural
energy associated to the solutions $u$ of the systems, the
nonexistence of global solutions, when the initial energy is
controlled above by a critical value was proved. And the
$p$-Kirchhoff equations involving the quasilinear homogeneous
$p$-Laplace operator were extended to the $p(x)$-Kirchhoff equations
which have been used in the last decades to model various

Key words: $p(x)$-Kirchhoff systems, global non-existence, nonlinear source and boundary damping terms

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