Oscillation for second-order half-linear delay damped dynamic equations on time scales

Autor: Jimeng Li, Jiashan Yang
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Zdroj: Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-12 (2019)
Druh dokumentu: article
ISSN: 1687-1847
DOI: 10.1186/s13662-019-2136-y
Popis: Abstract We investigate oscillation of second-order half-linear variable delay damped dynamic equations [a(t)|xΔ(t)|λ−1xΔ(t)]Δ+b(t)|xΔ(t)|λ−1xΔ(t)+p(t)|x(δ(t))|λ−1x(δ(t))=0 $$ \bigl[a(t) \bigl\vert x^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t) \bigr]^{\Delta }+b(t) \bigl\vert x ^{\Delta }(t) \bigr\vert ^{\lambda -1}x^{\Delta }(t)+p(t) \bigl\vert x \bigl(\delta (t) \bigr) \bigr\vert ^{\lambda -1}x \bigl(\delta (t) \bigr)=0 $$ on a time scale T $\mathbb{T}$. By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the equations under the condition ∫t0∞[a−1(s)e−b/a(s,t0)]1/λΔs
Databáze: Directory of Open Access Journals
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