A Composite Coincidence Degree with Applications to Boundary Value Problems of Neutral Equations

DOI10.2307/2154389zbMath0770.34053OpenAlexW4246981013MaRDI QIDQ4038482

Jianhong Wu, Lynn H. Erbe, Wiesław Krawcewicz

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2154389

zbMATH Keywords

boundary value problemsneutral equationstopological degree theoryessential mapretarded equationstopological transversality theorem of Granascomposite coincidence degreeunbounded Fredholm operator of index zero

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Degree theory for nonlinear operators (47H11) Neutral functional-differential equations (34K40) Boundary value problems for functional-differential equations (34K10) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (15)

Periodic solution of neutral Lotka-Volterra system with periodic delays ⋮ Existence of periodic solutions for neutral functional differential equations with nonlinear difference operator ⋮ Positive periodic solutions of periodic neutral Lotka-Volterra system with state dependent delays ⋮ A new existence theory for positive periodic solutions to a class of neutral delay model with feedback control and impulse ⋮ Boundary value problems for impulsive differential equations ⋮ On positive periodic solutions of a nonautonomous neutral delay \(n\)-species competitive system ⋮ Levinson’s Problem on Affine-Periodic Solutions ⋮ Existence of positive periodic solutions for a nonautonomous neutral delay n-species competitive model with impulses ⋮ Positive periodic solutions for a neutral Lotka-Volterra system with state dependent delays ⋮ Positive Periodic Solutions of N-Species Neutral Delay Systems ⋮ Periodicity on a class of neutral impulsive delay system ⋮ Global continua of periodic solutions to some difference-differential equations of neutral type ⋮ Existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch systems with stocking ⋮ Periodic solutions for dissipative-repulsive systems ⋮ Topological transversality and periodic solutions of neutral functional differential equations

Cites Work

• A boundary value problem for functional differential equations of delay type
• Some criteria for the existence of periodic oscillations in nonlinear systems
• Coincidence degree, and nonlinear differential equations
• Coincidence degree and periodic solutions of neutral equations
• Periodic solutions of nonlinear functional differential equations
• The fixed point index for local condensing maps
• Degree theory for local condensing maps
• Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces
• Equations with bounded nonlinearities
• Periodic solutions of hereditary differential systems
• Leray-Schauder degree for semilinear Fredholm maps and periodic boundary value problems of neutral equations
• A Note on Periodic Solutions for Delay-Differential Systems
• The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
• Two Point Boundary Value Problems for Nonlinear Functional Differential Equations
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