Oscillation for Higher Order Dynamic Equations on Time Scales
We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficien...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/268721 |
| Summary: | We investigate the oscillation of the following higher order dynamic equation: {an(t)[(an-1(t)(⋯(a1(t)xΔ(t))Δ⋯)Δ)Δ]α}Δ+p(t)xβ(t)=0, on some time scale T, where n≥2, ak(t) (1≤k≤n) and p(t) are positive rd-continuous functions on T and α,β are the quotient of odd positive integers. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero. |
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| ISSN: | 1085-3375 1687-0409 |