Uniform ultimate boundedness and periodicity in functional differential equations

DOI10.2748/tmj/1178227696zbMath0678.34073OpenAlexW1987527264MaRDI QIDQ1124032

Bo Zhang, Theodore Allen Burton

Publication date: 1990

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178227696

zbMATH Keywords

Banach spacefunctional differential equationsHorn's fixed point theoremuniformly ultimately bounded solutions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (13)

Boundedness, periodicity, and convergence of solutions in a retarded Liénard equation ⋮ Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems ⋮ ON THE NUMBER OF POSITIVE PERIODIC SOLUTIONS OF FUNCTIONAL DIFFERENTIAL EQUATIONS AND POPULATION MODELS ⋮ Boundedness in functional differential equations ⋮ Periodic oscillation for discrete-time Hopfield neural networks ⋮ Periodic solutions of difference equations ⋮ Positive periodic solutions for a class of delay differential equations ⋮ Existence of periodic solutions in distribution for stochastic Newtonian systems ⋮ Wong-Zakai approximations and periodic solutions in distribution of dissipative stochastic differential equations ⋮ Stability and boundedness in difference systems with finite delay ⋮ Fréchet phase space for nonlinear infinite delay equations in Banach spaces ⋮ Periodic solutions to convex neutral functional-differential equations ⋮ Topological transversality and periodic solutions of neutral functional differential equations

Cites Work

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• On a generalization of the Schauder fixed point theorem
• Stability and periodic solutions of ordinary and functional differential equations
• An autonomous system whose solutions are uniformly ultimately bounded but not uniformly bounded
• Liapunov-Razumikhin conditions for stability and boundedness of functional differential equations of Volterra type
• Fixed point theorems and dissipative processes
• The existence of periodic solutions of systems of differential equations
• Transformation theory of non-linear differential equations of the second order
• Periodic Solutions of Functional Differential Equations with Infinite Delay
• Periodic solutions to functional differential equations
• Some Fixed Point Theorems for Compact Maps and Flows in Banach Spaces

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