Computational fixed-point theory for differential delay equations with multiple time lags
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Publication:665977
DOI10.1016/j.jde.2011.11.020zbMath1247.34119OpenAlexW2003645160MaRDI QIDQ665977
Gábor Kiss, Jean-Philippe Lessard
Publication date: 7 March 2012
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2011.11.020
Fourier expansiondelay equationcontraction mapping theoremmultiple time lagsNewton-type operatorradii polynomials
Applications of operator theory to differential and integral equations (47N20) Periodic solutions to functional-differential equations (34K13)
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Cites Work
- Unnamed Item
- Periodic solutions of delay equations with several fixed delays
- Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
- The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
- Stability implications of delay distribution for first-order and second-order systems
- Validated continuation over large parameter ranges for equilibria of PDEs
- Numerical methods in bifurcation problems. Lectures delivered at the Indian Institute of Science, Bangalore, under the T.I.F.R.-I.I.Sc. Programme in Applications of Mathematics. Notes by A. K. Nandakumaran and Mythily Ramaswamy
- Periodic solutions of analytic functional differential equations are analytic
- A global bifurcation theorem with applications to functional differential equations
- Periodic solutions for functional differential equations with multiple state-dependent time lags
- Delay equations. Functional-, complex-, and nonlinear analysis
- Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
- Global dynamics of delay differential equations
- Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation
- A further generalization of the Schauder fixed point theorem
- Some global results for nonlinear eigenvalue problems
- NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
- Rigorous Numerics for Symmetric Connecting Orbits: Even Homoclinics of the Gray–Scott Equation
- Validated Continuation for Equilibria of PDEs
- INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS
- Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift–Hohenberg Equation
- A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations
- Differential-delay equations with two time lags
- A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
- The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
- Computer-assisted enclosure methods for elliptic differential equations
