Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Existence of Positive Solutions for a Class of Higher Order Neutral Functional Differential Equations

Authors:

Satoshi Tanaka

Affiliation:

(1) Graduate School of Science and Engineering, Doctor Course, Ehime University, Matsuyama, 790-8577, Japan;(2) Present address: Department of Liberal Arts and Engineering Science, Hachinohe National College of Technology, Hachinohe, 039-1192, Japan

Abstract:

The higher order neutral functional differential equation

$(1) frac {d^n}{dt^n} [x(t)+ h(t)x ( tau(t))]+ sigma f (t,x (g(t)))=0$

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).

Keywords:

neutral differential equation positive solution

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