A Class of Singular Neutral-Differential Systems

A Matrix Method for Determining Eigenvalues and Stability of Singular Neutral Delay-Differential Systems

A note on a class of singular integro-differential equations

in which ak'S and bk'S are complex constants,fk(x) represents the kth derivative of the unknown function f(x) with prescribed initial valuesfk(0), along with the conditions thatfk(oo) = 0, for k = 0, 1, 2 . . . . . n, and 9(x) represents a known differentiable function arises in a natural way while solving a class of mixed boundary value problems of mathematical physics (see [-3, 5, 6]). Varley...

Spectral Properties of a Class of Singular Differential Operators

We consider the operator A0f = (−1)n 1 v(t) ( Dρ )∗ [ u(t)Dρ ( f (t) v(t) )] , where Dρ f (t) = dk dtk [ ρ(t) dmf (t) dtm ] , ( Dρ )∗ f (t) = dm dtm [ ρ(t) dkf (t) dtk ] , k + m = n. Our main aim is to prove some spectral properties of a natural extension of this operator. In order to prove this we need to prove some properties of a function space, connected to the operator Dρ , and some embedd...

Existence of bounded solutions of a class of neutral systems of functional differential equations

System of functional differential equations Iterated deviations Lipschitz derivative a b s t r a c t Some results on the existence of bounded solutions together with their first derivatives of a class of neutral systems of functional differential equations with complicated deviations, which extend and unify numerous results in the literature, are proved.

The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays

We study a kind of vector singular perturbed delay-differential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at t = σ. Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.