Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations
نویسندگان
چکیده
منابع مشابه
Existence of Nonoscillatory Bounded Solutions for a System of Second-order Nonlinear Neutral Delay Differential Equations
A system of second-order nonlinear neutral delay differential equations ( r1(t) ( x1(t) + P1(t)x1(t− τ1) )′)′ = F1 ( t, x2(t− σ1), x2(t− σ2) ) , ( r2(t) ( x2(t) + P2(t)x2(t− τ2) )′)′ = F2 ( t, x1(t− σ1), x1(t− σ2) ) , where τi > 0, σ1, σ2 ≥ 0, ri ∈ C([t0,+∞),R), Pi(t) ∈ C([t0,+∞),R), Fi ∈ C([t0,+∞)× R2,R), i = 1, 2 is studied in this paper, and some sufficient conditions for existence of nonosc...
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Throughout this paper, the following conditions are assumed to hold. () n≥ is a positive integer, r ∈ C([t,∞),R+), < a < b, τ > , σ > ; () p ∈ C([t,∞)× [a,b],R), q ∈ C([t,∞),R+), q ∈ C([t,∞),R+), h ∈ C([t,∞),R); () (u) is a continuously increasing real function with respect to u defined on R, and –(u) satisfies the local Lipschitz condition; () gi ∈ C(R,R), gi(u) satisfy the l...
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where n ≥ is an integer, τ > , σ ≥ , d > c ≥ , b > a ≥ , r, P ∈ C([t,∞), (,∞)), P ∈ C([t,∞)× [a,b], (,∞)), Q ∈ C([t,∞), (,∞)), Q ∈ C([t,∞)× [c,d], (,∞)), f ∈ C(R,R), f is a nondecreasing function with xf (x) > , x = . The motivation for the present work was the recent work of Culáková et al. [] in which the second-order neutral nonlinear differential equation of the form [ ...
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This paper deals with the first order neutral delay differential equation (x(t) + a(t)x(t− τ))′ + p(t)f(x(t− α)) +q(t)g(x(t − β)) = 0, t ≥ t0, Using the Banach fixed point theorem, we show the existence of a bounded nonoscillatory positive solution for the equation. Three nontrivial examples are given to illustrate our results. Mathematics Subject Classification: 34K4
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Nonoscillatory solutions of a general class of second order functional neutral differential equations of the form
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2005
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-005-0018-9