Existence and uniqueness theorems for some functional differential equations of neutral type

DOI10.1016/0022-0396(72)90070-8zbMath0263.34070OpenAlexW1980498162MaRDI QIDQ2561330

Roger D. Nussbaum

Publication date: 1972

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(72)90070-8

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) General theory of functional-differential equations (34K05)

Related Items (14)

On pantograph integro-differential equations ⋮ Semi-hyperbolic mappings, condensing operators, and neutral delay equations ⋮ A new method based on the RKHSM for solving systems of nonlinear IDDes with proportional delays ⋮ Existence of solutions for a nonlinear nonlocal hybrid functional fractional differential equation ⋮ Condensing operators ⋮ Analytic solutions to a class of nonlinear infinite-delay-differential equations ⋮ On neutral functional-differential equations with proportional delays ⋮ Direct operatorial tau method for pantograph-type equations ⋮ Periodic solutions of some nonlinear, autonomous functional differential equations. II ⋮ Periodic solutions of some nonlinear autonomous functional differential equations ⋮ Existence of periodic solutions of one-dimensional differential-delay equations ⋮ Two further applications of the edelstein fixed point theorem to initial value problems of functional equations ⋮ Regular solutions of the Shabat equation ⋮ Theory of equations of neutral type

Cites Work

• Existence and continuous dependence of solutions of a neutral functional- differential equation
• Existence, uniqueness and continuous dependence for hereditary systems
• A generalization of the Ascoli theorem and an application to functional differential equations
• The fixed point index for local condensing maps
• Degree theory for local condensing maps
• A class of neutral functional differential equations
• Properties of linear transformations preserved under addition of a completely continuous transformation
• Punti uniti in trasformazioni a codominio non compatto
• The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
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