Existence of nonoscillatory solutions to neutral dynamic equations on time scales. (English) Zbl 1128.34043

The authors study the existence of a positive solution for the neutral functional dynamic equation on time scale
\[ [x(t)+p(t)x(g(t))]^{\Delta}+f(t,x(h(t))=0.\tag{1} \]
Here is one of the results of the paper.
Theorem. Equation (1) has an eventually positive solution \(x(t)\) with \(\lim_{t\rightarrow\infty}x(t)=a>0 \) if and only if there exists a constant \(K>0\) such that \[ \int_{t_0}^{\infty}\Delta s <\infty. \]


34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
39A10 Additive difference equations
Full Text: DOI


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