A note on partial functional differential equations with state-dependent delay

DOI10.1016/j.nonrwa.2005.03.014zbMath1109.34060OpenAlexW2004825879MaRDI QIDQ859551

Andréa Prokopczyk, Eduardo M. Hernández, Luiz A. C. Ladeira

Publication date: 16 January 2007

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2005.03.014

zbMATH Keywords

mild solutionsfunctional-differential equationsunbounded delaystate-dependent delay

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Partial functional-differential equations (35R10) Functional-differential equations in abstract spaces (34K30)

Related Items (72)

A study of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces ⋮ On abstract neutral differential equations with state-dependent delay ⋮ Solvability and optimal controls of non-instantaneous impulsive stochastic neutral integro-differential equation driven by fractional Brownian motion ⋮ Controllability of multi-term time-fractional differential systems with state-dependent delay ⋮ Global existence results for neutral functional differential equations with state-dependent delay ⋮ Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay ⋮ Existence and uniqueness of solution for abstract differential equations with state-dependent delayed impulses ⋮ Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay ⋮ On abstract differential equations with state dependent non-local conditions ⋮ \(C^{1+\alpha}\)-strict solutions and wellposedness of abstract differential equations with state dependent delay ⋮ Existence results for partial neutral functional differential equations with state-dependent delay ⋮ -ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY ⋮ Global existence results for second order functional differential equations with delay ⋮ Existence of integro-differential solutions for a class of abstract partial impulsive differential equations ⋮ On state-dependent delay partial neutral functional--differential equations ⋮ Functional implicit hyperbolic fractional order differential equations with delay ⋮ Nonlinear impulsive partial functional differential inclusions with state-dependent delay and multivalued jumps ⋮ Approximate controllability of semilinear non-autonomous evolution systems with state-dependent delay ⋮ Existence and uniqueness of solution for abstract differential equations with state-dependent time impulses ⋮ Existence results for a coupled system of fractional integro-differential equations with time-dependent delay ⋮ Existence results for the solution of abstract neutral impulsive differential problems with state-dependent delay ⋮ Existence and uniqueness of global solution for abstract second order differential equations with state‐dependent delay ⋮ Existence of solutions for fractional partial neutral stochastic functional integro-differential inclusions with state-dependent delay and analytic resolvent operators ⋮ Results on controllability and well-posedness of functional abstract second-order differential equations with state-dependent delay ⋮ Controllability of neutral evolution integrodifferential systems with state dependent delay ⋮ Existence results for an impulsive abstract partial differential equation with state-dependent delay ⋮ Non-Instantaneous Impulsive Fractional Integro-Differential Equations with State-Dependent Delay ⋮ Non-local PDEs with a state-dependent delay term presented by Stieltjes integral ⋮ Результаты существования для функционально возмущенных дифференциальных уравнений дробного порядка с запаздыванием в банаховых пространствах ⋮ A study on existence of solutions for fractional functional differential equations ⋮ Wellposedness of impulsive functional abstract second-order differential equations with state-dependent delay ⋮ Local and global existence and uniqueness of solution for abstract differential equations with state-dependent argument ⋮ On Fractional Integro-differential Equations with State-Dependent Delay and Non-Instantaneous Impulses ⋮ Abstract neutral differential equations with state‐dependent delay and almost sectorial operators ⋮ Measure of noncompactness and partial functional differential equations with state-dependent delay ⋮ A condition on delay for differential equations with discrete state-dependent delay ⋮ Existence of solutions for impulsive partial stochastic neutral integrodifferential equations with state-dependent delay ⋮ Global existence for functional differential equations with state-dependent delay ⋮ On fractional integro-differential equations with state-dependent delay ⋮ Existence results for fractional neutral integro-differential equations with state-dependent delay ⋮ Existence results for some partial functional differential equations with state-dependent delay ⋮ On evolutionary Volterra equations with state-dependent delay ⋮ Unnamed Item ⋮ Global existence and stability for functional evolution equations with state-dependent delay ⋮ On fractional integro-differential inclusions with state-dependent delay in Banach spaces ⋮ Equivalence of the MTS Method and CMR Method for Differential Equations Associated with Semisimple Singularity ⋮ Solvability for impulsive neutral integro-differential equations with state-dependent delay via fractional operators ⋮ Existence results for a fractional equation with state-dependent delay ⋮ Existence results for an impulsive neutral functional differential equation with state-dependent delay ⋮ On state-dependent delay partial neutral functional integro-differential equations ⋮ Approximate controllability of partial neutral functional differential systems of fractional order with state-dependent delay ⋮ Mild solutions for impulsive neutral functional differential equations with state-dependent delay ⋮ Non-linear partial differential equations with discrete state-dependent delays in a metric space ⋮ On second order differential equations with state-dependent delay ⋮ Approximate controllability of impulsive fractional stochastic differential equations with state-dependent delay ⋮ Controllability of fractional integrodifferential equations with state-dependent delay ⋮ EXISTENCE RESULTS FOR NONDENSELY DEFINED IMPULSIVE SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY ⋮ Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay ⋮ Abstract Volterra equations with state-dependent delay ⋮ Existence and uniqueness of solutions for abstract neutral differential equations with state-dependent delay ⋮ Well-posedness of abstract integro-differential equations with state-dependent delay ⋮ Differential equations with discrete state-dependent delay: Uniqueness and well-posedness in the space of continuous functions ⋮ Global existence results for neutral functional differential inclusions with state-dependent delay ⋮ Unnamed Item ⋮ Approximate controllability of the non-autonomous impulsive evolution equation with state-dependent delay in Banach spaces ⋮ Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces ⋮ Existence results for a class of impulsive neutral fractional stochastic integro-differential systems with state dependent delay ⋮ Impulsive fractional differential inclusions with state-dependent delay ⋮ Existence of solutions for some nonautonomous partial functional differential equations with state-dependent delay ⋮ Existence, uniqueness and approximate controllability of abstract differential equations with state-dependent delay ⋮ Approximate controllability of neutral delay integro-differential inclusion of order \(\alpha\in (1, 2)\) with non-instantaneous impulses ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• Functional differential equations with infinite delay
• Introduction to functional differential equations
• Periodicity in a food-limited population model with toxicants and state dependent delays.
• Periodic solutions for delay Lotka-Volterra competition systems
• A mathematical model of the dynamics of the phytoplankton-nutrient system
• On equations with delay depending on solution
• Linearized stability in periodic functional differential equations with state-dependent delays
• Theory and applications of partial functional differential equations
• Periodic solutions for differential equations with state-dependent delay and positive feedback
• Parameter estimation by quasilinearization in functional differential equations with state-dependent delays: a numerical study.
• Parameter identification in classes of neutral differential equations with state-dependent delays
• Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay
• The effects of state-dependent time delay on a stage-structured population growth model
• Positive almost periodic solutions of a state-dependent delay nonlinear integral equation
• Identification of parameters in delay equations with state-dependent delays
• Slowly oscillating periodic solutions of autonomous state-dependent delay equations

This page was built for publication: A note on partial functional differential equations with state-dependent delay