Asymptotic behavior of solutions of third-order nonlinear dynamic equations on time scales

Authors:
Zhi-Hua Yu;Qi-Ru Wang
Affiliations:
Department of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong 510275, PR China;Department of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong 510275, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 1
Cited 1

Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales

Journal of Computational and Applied Mathematics

Asymptotic properties of solutions of certain third-order dynamic equations

Journal of Computational and Applied Mathematics

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Abstract

In this paper, we will study asymptotic behavior of solutions to third-order nonlinear dynamic equations on time scales of the form (1a"2(t)((1a"1(t)(x^@D(t))^@a^"^1)^@D)^@a^"^2)^@D+q(t)f(x(t))=0. By using the Riccati technique and integral averaging technique, two different types of criteria are established, one of which extends some existing results and the other is new. Two examples of dynamic equations on different time scales are given to show the applications of the obtained results.