Asymptotic behavior of nonlinear delay-differential equations

Asymptotic Behavior of Solutions of Nonlinear Delay Differential Equations With Impulse

This paper studies the asymptotic behavior of solutions of the second-order nonlinear delay differential equations with impulses: 1 ( ( ) ( )) ( ) ( ) ( ) ( ) ( ) 0 n i i k i r t x t p t x t q t x t f t t t σ ′ ′ ′ = − + − + = , ≠ , ∑ ( ) ( ) ( ) ( ) ( ) ( ) k k k k k k k k x t x t a x t x t x t b x t k Z ′ ′ ′ + + + − = , − = , ∈ . and some sufficient conditions are obtained. Keywords-Asymptot...

Oscillation and Asymptotic Behavior of Solutions of Nth Order Nonlinear Delay Differential Equations*

where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...

Asymptotic Behavior of the Solutions of Nonlinear Differential Equations

3. J. S. MacNerney, Stieltjes integrals in linear spaces, Ann. of Math. (2) 61 (1955), 354-367. 4. -, Continuous products in linear spaces, J. Elisha Mitchell Sei. Soc. 71 (1955), 185-200. 5. ■-, Determinants of harmonic matrices, Proc. Amer. Math. Soc. 7 (1956), 1044-1046. 6. F. W. Stallard, Differential systems with interface conditions, Oak Ridge National Laboratory Publication no. 1876 (Phy...

Asymptotic Behavior of Solutions of Nonlinear Functional Differential Equations

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equation du(t)/dt + Au(t)+ G(u)(t) f(t), where A is a maximal monotone operator in a nilbert space H,f E LI(0,:H) and G:C([O,c):D(A))LI(O,c:H)is a given mapping.

Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations