Publication details

Function sequence technique for half-linear dynamic equations on time scales

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Year of publication 2006
Type Article in Periodical
Magazine / Source Panamer. Math. J.
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords half-linear equation; time scale; oscillation criteria
Description We develop the method involving certain function sequences that, combined with the Riccati technique, provides a new tool for investigation of oscillatory properties of half-linear dynamic equations on time scales. As applications, we give various new oscillation and nonoscillation criteria (e.g., of Hille-Nehari type and of Willett type), and comparison theorems. In addition to the aspect of unification and extension, many of the results turn out to be new in the discrete case and in the linear time scale case; some of the observations are new even in the continuous case. An oscillation criterion which applies when ``usual'' criteria fail, and four examples illustrating our results are given as well.
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