Abstract
The higher order neutral functional differential equation
is considered under the following conditions: \(n \geqslant 2, \sigma = \pm 1, \tau (t)\) is strictly increasing in \(t \in \left[ {t_0 ,\infty } \right), \tau (t) < t {\text{for}} t \geqslant t_0 ,\mathop { \lim }\limits_{t \to \infty } \tau (t) = \infty ,\mathop { \lim }\limits_{t \to \infty } g(t) = \infty , {\text{and}} f(t,u)\) is nonnegative on \(\left[ {t_0 ,\infty } \right) \times \left( {0,\infty } \right)\) and nondecreasing in \(u \in (0,\infty )\). A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).
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Tanaka, S. Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations. Czechoslovak Mathematical Journal 51, 573–583 (2001). https://doi.org/10.1023/A:1013736122991
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DOI: https://doi.org/10.1023/A:1013736122991