Oscillatory Property of n-th Order Functional Differential Equations |
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Authors: | George W Johnson and Yan Jurang |
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Institution: | Department of Mathematics and Statistics, University of South Carolona. and Department of Mathematics, Shanxi University, Taiyuan, China. |
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Abstract: | The authors study oscillatory property of nonlinear functional differential equation
$L_nx(t)+p(t)f(x(t),x(g(t)))=r(t)$(1)
where L_nx(t) is an n-th order linear differential operator defined by
$L_0x(t)=x(t)$,
$L_kx(t)=\frac{d}{dt}(a_k-1(t)L_k-1x(t)),k=1,2,\cdots,n.$
Sufficient conditions are obtained which guarantee that all continuable solutions of (1) are oscillatory or tend to zero as t\rightarrow \infinity. |
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Keywords: | |
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