Existence of nonoscillatory solutions of first order nonlinear neutral equations
Lu Wudu
(Received September 1989; revised February 1990)
Abstract
Consider the nonlinear neutral equation
m n
(x(t) - å pi (t) x(hi(t)))' +
å fj (t, x(gj(t))) = Q(t) i=1 j=1
where pi (t), hi (t), gj (t), Q(t) Î C[t0, ¥),
lim t®¥ hi (t) = ¥, lim t®¥ gj (t) = ¥,
i Î Im = {1, 2, ¼, m}, j Î In = {1, 2, ¼, n}.
We obtain a necessary and sufficient condition (2) for this equation to have a nonoscillatory solution x(t)
with lim t®¥ inf |x(t)| > 0 (Theorems 5
and 6) or to have a bounded nonoscillatory solution x(t)
with lim t®¥ inf |x(t)| > 0 (Theorem 7).
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Author
Lu Wudu
Department of Mathematics, South China Normal University, Guangzhou, 510631, China.
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