Oscillation of solutions for third order functional dynamic equations
In this article we study the oscillation of solutions to the third order nonlinear functional dynamic equation $$ L_{3}(x(t))+sum_{i=0}^{n}p_i(t)Psi_k{alpha_ki}(x(h_i(t)))=0, $$ on an arbitrary time scale $mathbb{T}$. Here $$ L_0(x(t))=x(t),quad L_k(x(t))=Big(frac{[ L_{k-1}x(t)]^{Delta }}{a_...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2010-09-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2010/131/abstr.html |
| Summary: | In this article we study the oscillation of solutions to the third order nonlinear functional dynamic equation $$ L_{3}(x(t))+sum_{i=0}^{n}p_i(t)Psi_k{alpha_ki}(x(h_i(t)))=0, $$ on an arbitrary time scale $mathbb{T}$. Here $$ L_0(x(t))=x(t),quad L_k(x(t))=Big(frac{[ L_{k-1}x(t)]^{Delta }}{a_k(t)}Big)^{gamma_kk}, quad k=1,2,3 $$ with $a_1, a_2$ positive rd-continuous functions on $mathbb{T}$ and $a_{3}equiv 1$; the functions $p_i$ are nonnegative rd-continuous on $mathbb{T}$ and not all $p_i(t)$ vanish in a neighborhood of infinity; $Psi_k{c}(u)=|u|^{c-1}u$, $c>0$. Our main results extend known results and are illustrated by examples. |
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| ISSN: | 1072-6691 |