Oscillation criteria of second-order quasi-linear neutral delay differential equations
نویسندگان
چکیده
منابع مشابه
Oscillation criteria for second order quasi-linear neutral delay differential equations
New oscillation criteria for the second order nonlinear neutral delay differential equation [y(t) + p(t)y(t− τ)]′′ + q(t) f(y(g(t))) = 0, t ≥ t0 are given. The relevance of our theorems becomes clear due to a carefully selected example.
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Some sufficient conditions are established for the oscillation of second-order neutral differential equation x t p t x τ t ′′ q t f x σ t 0, t ≥ t0, where 0 ≤ p t ≤ p0 < ∞. The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 1985 , Grace and Lalli 1987 , Ruan 1993 , H. J. Li 1996 ...
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Oscillation criteria for the higher order quasi-linear neutral delay differential equations of the form [r(t)ψ(u(t))|z(n−1)(t)|α−1z(n−1)(t)]′ + m ∑ i=1 qi(t) fi(|u(τi(t))|αi−1u(τi(t))) = 0, t t0, z(t) = u(t) + p(t)u(t −σ),α > 0,αi > 0 (i = 1,2,3, ...,m) , are established under the condition: ∫ ∞ t0 r− 1 α (s)ds = ∞ or ∫ ∞ t0 r− 1 α (s)ds < ∞ respectively, where n is even. The obtained results i...
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In this paper, some new oscillation criteria are obtained for the secondorder quasi-linear neutral delay differential equation ( r(t)| ( x(t) + p(t)x(τ(t)) )′|α−1(x(t) + p(t)x(τ(t)))′)′+ f ( t, x(σ(t)) ) = 0, t ≥ t0 under the case when ∫∞ t0 1 r 1 α (t) dt <∞. Our results improve and supplement some known results in the literature. An example is also provided to illustrate the main results.
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In this paper we will establish some oscillation criteria for the second-order nonlinear neutral delay dynamic equation ( r(t) (( y(t)+ p(t)y(t − τ))∆)γ )∆ + f (t, y(t − δ))= 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r(t) and p(t) real-valued positive functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of the...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2007
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2006.11.014