数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (4): 975-988.doi: 10.1016/S0252-9602(13)60056-9

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OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

Taher S. HASSAN|Qingkai KONG   

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt; Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
  • 收稿日期:2012-06-04 出版日期:2013-07-20 发布日期:2013-07-20
  • 基金资助:

    The second author is supported in part by the NNSF of China (10971231 and 11271379).

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DYNAMIC EQUATIONS WITH p-LAPLACIAN AND DAMPING

Taher S. HASSAN|Qingkai KONG   

  1. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt; Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
  • Received:2012-06-04 Online:2013-07-20 Published:2013-07-20
  • Supported by:

    The second author is supported in part by the NNSF of China (10971231 and 11271379).

摘要:

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping
(r(t)φα(xΔ(t))Δ+ p (t)φα(xΔα(t)+ q(t)f (xα(t)) = 0
on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.

关键词: oscillation, dynamic equations, time scales

Abstract:

This paper concerns the oscillation of solutions of the second order nonlinear dynamic equation with p-Laplacian and damping
(r(t)φα(xΔ(t))Δ+ p (t)φα(xΔα(t)+ q(t)f (xα(t)) = 0
on a time scale T which is unbounded above. Sign changes are allowed for the coefficient functions r, p and q. Several examples are given to illustrate the main results.

中图分类号: 

  • 34K11