Existence results for partial neutral functional integrodifferential equations with unbounded delay

We prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the Leray-Schauder alternative.     

Existence results for an impulsive neutral functional differential equation with state-dependent delay

In this article, we study the existence of mild solutions for a class of impulsive abstract partial neutral functional differential equations with state-dependent delay. The results are obtained by using Leray–Schauder Alternative fixed point theorem.     

Differentiability of solutions of second-order functional differential equations with unbounded delay

In this paper we study the differentiability of solutions of the second-order semilinear abstract retarded functional differential equation with unbounded delay, specially when the underlying space is reflexive or at least has the Radon–Nikodym property. We apply our results to characterize the infinitesimal generators of several strongly continuous semigroups of linear operators that arise in the theory of linear abstract retarded functional differential equations with unbounded delay on a phase space defined axiomatically.     

Existence of solutions for abstract neutral integro-differential equations with unbounded delay

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.     

On state-dependent delay partial neutral functional integro-differential equations

In this paper the existence of mild solutions for a class of abstract neutral integro-differential equations with state-dependent delay is studied.     

Existence results for a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay

In this paper, a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay is introduced.Under some dissipative conditions, we obtain the existence, uniqueness and continuous dependence of mild solutions for these equations. An application involving a fractional stochastic parabolic system with not instantaneous impulses is considered.     

Hopf bifurcation analysis of integro-differential equation with unbounded delay

The complexity of a nonlinear dynamical system is controllable via a selection of system parameters. One representative behavior of such a complex system can be illustrated by Hopf bifurcation. This paper presents a Hopf bifurcation analysis of a kind of integro-differential equations with unbounded delay. Based on the Hopf bifurcation principle, a set of relationships among system parameters are obtained when a periodic orbit exists in the system. A numerical analysis is applied to solve the integro-differential delay equation. This paper proves the existence of Hopf bifurcation in the corresponding difference equations under the same system parameters as that in the integro-differential delay equations.     

Existence results for partial neutral functional differential equations with state-dependent delay

In this paper we study the existence of mild solutions for a class of first order abstract partial neutral differential equations with state-dependent delay.     

Existence results for a nondensely-defined impulsive neutral differential equation with state-dependent delay

In this paper, we prove the existence of integral solutions for a first order nondensely-defined impulsive neutral differential equation with state-dependent delay. The results are obtained by using suitable fixed point theorems. As applications of these main theorems, some consequences are obtained for the sub-linear growth cases.     

Existence of solutions for impulsive partial neutral functional differential equation with infinite delay

In this paper, the existence of mild solutions for first-order impulsive semilinear neutral functional differential equations with infinite delay in Banach spaces is investigated. We derive conditions in respect of the Hausdorff measure of noncompactness under which the mild solutions exist in Banach spaces. Our results improve and generalize some previous results.     

Existence results of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces

This paper investigates a class of second-order impulsive neutral functional integrodifferential inclusions with unbounded delay in Banach spaces. The existence of mild solutions of these inclusions is determined by using the theory of cosine families of bounded linear operators and a recent fixed point theorem for multivalued maps due to Dhage.     

Existence results for a degenerated nonlinear elliptic partial differential equation

The aim of this paper is to establish the existence of weak solutions to a steady state two-dimensional irrotational compressible flow around a thin profile. This flow is described by the small disturbance equations. If the speed of sound exceeds the fluid one, the governing equations remain elliptic. But when the fluid speed is beyond the sound one, the flow becomes locally hyperbolic and shock waves arise. For a modified elliptic model, using convexity arguments, we prove the existence of a solution which is the solution to the first model when the flow remains subsonic.     

Existence of solutions for impulsive partial neutral functional differential equations

This paper is concerned with partial neutral functional differential equations of first and second order with impulses. We establish some results of existence of mild solutions for these classes of equations.     

Existence of periodic solutions for abstract neutral non-autonomous equations with infinite delay

In this paper, by using Sadovskii fixed point theorem, we study the existence of solutions and periodic solutions for a class of abstract neutral functional evolution equations with infinite delay. An example is presented in the end to show the applications of the obtained results.     

The Cauchy problem for a singularly perturbed Volterra integro-differential equation

The Cauchy problem for a singularly perturbed Volterra integro-differential equation is examined. Two cases are considered: (1) the reduced equation has an isolated solution, and (2) the reduced equation has intersecting solutions (the so-called case of exchange of stabilities). An asymptotic expansion of the solution to the Cauchy problem is constructed by the method of boundary functions. The results are justified by using the asymptotic method of differential inequalities, which is extended to a new class of problems.     

Existence of some neutral partial differential equations with infinite delay

This study intends to investigate a class of quasi-linear partial neutral functional differential equations with infinite delay. We assume that the linear part generates an analytic compact semigroup and the nonlinear part satisfies certain conditions. A sufficient condition is given to ensure the existence of mild and classical solutions. Finally, an example is given to illustrate our abstract results.     

Existence results for impulsive neutral evolution integrodifferential equations with infinite delay

In this paper we prove the existence of mild solutions for impulsive neutral evolution integrodifferential equations with infinite delay in Banach spaces. The results are obtained by using the analytic semigroup theory and the Krasnoselski–Schaefer type fixed point theorem. An example is provided to illustrate the theory.     

Existence results for impulsive neutral functional differential equations with infinite delay

In this work, we prove the existence of mild solutions for impulsive partial neutral functional differential equations with infinite delay in a Banach space. The results are obtained by using the Krasnoselski–Schaefer type fixed point theorem.     

On the application of substochastic semigroup theory to fragmentation models with mass loss

A linear integro-differential equation modelling multiple fragmentation with inherent mass loss is investigated by means of substochastic semigroup theory. The existence of a semigroup is established and, under natural conditions on certain coefficients, the generator of this semigroup is identified. This yields, in particular, a validation of the formal mass-loss rate equation for the model.     

Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay

In this article, we investigate the existence and asymptotic stability in p-th moment of a mild solution to a class of neutral stochastic integro-differential equation of fractional order involving non-instantaneous impulses with infinite delay in a Hilbert space. A new set of sufficient conditions proving existence and asymptotic stability of mild solution is derived by utilizing solution operator, functional analysis, stochastic analysis and fixed point technique. Finally, an example is provided to illustrate the obtained abstract result.