In this work, we study the oscillation of fourth order neutral differential equations with delay argument. By means generalized Riccati transformation technique, obtain new criteria for equation. An example is given to clarify main results in paper.

Abstract In this paper, we obtain necessary and sufficient conditions for the oscillation of solutions to a second-order neutral differential equation with impulses. Two examples are provided show effectiveness feasibility main results. Our tool is Lebesgue’s dominated convergence theorem.

The time-dependent Maxwell system is supplemented with the constitutive relations of linear bianisotropic media and is treated as a neutral integro-differential equation in a Hilbert space. By using the theory of abstract Volterra equations and strongly continuous semigroups we obtain general well-posedness results for the corresponding mathematical problem.

We use Krasnoselskii’s fixed point theorem to show that the nonlinear neutral differential equation with delay d dt [x(t)− ax(t− τ)] = r(t)x(t)− f(t, x(t− τ)) has a positive periodic solution. An example will be provided as an application to our theorems. AMS Subject Classifications: 34K20, 45J05, 45D05

This paper is concerned with the controllability result of mild solution for an impulsive neutral fractional order stochastic integro-differential equation with infinite delay subject to nonlocal conditions. The existence result is obtained by using the fixed point technique on a Hilbert space. At last, we present an example to verify the result. MSC: 93B05 • 26A33 • 34K05 • 34A37 • 34K50

In this paper the authors study the existence and asymptotic stability in p-th moment of mild solutions to stochastic neutral partial differential equation with impulses. Their method for investigating the stability of solutions is based on the fixed point theorem.

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.