Oscillation criteria of second-order half-linear dynamic equations on time scales

  • Authors:

  • S. H. Saker

  • Affiliations:

  • Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

In this paper, by using the Riccati transformation technique, chain rule and inequalityA^@l-@lAB^@l^-^1+(@l-1)B^@l=0,@l1,where A and B are positive constants, we will establish some oscillation criteria for the second-order half-linear dynamic equation(p(t)(x^@D(t))^@c)^@D+q(t)x^@c(t)=0,t@?[a,b]on time scales, where @c1 is an odd positive integer. Our results not only unify the oscillation of half-linear differential and half-linear difference equations but can be applied on different types of time scales and improve some well-known results in the difference equation case. Some examples are considered here to illustrate our main results.