Asymptotic stability for abstract nonlinear functional differential equations
- 1 January 1976
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 54 (1) , 225-230
- https://doi.org/10.2307/2040790
Abstract
The nonlinear autonomous functional differential equation <!-- MATH $\dot x(t) = f(x(t)) + g({x_t}),t \geqslant 0,{x_0} = \phi$ --> is investigated by means of the theory of semigroups of nonlinear operators. The properties of the semigroup associated with this equation provide stability information about the solutions.
Keywords
This publication has 6 references indexed in Scilit:
- Existence and Stability for Partial Functional Differential EquationsTransactions of the American Mathematical Society, 1974
- Autonomous nonlinear functional differential equations and nonlinear semigroupsJournal of Mathematical Analysis and Applications, 1974
- Generation of Semi-Groups of Nonlinear Transformations on General Banach SpacesAmerican Journal of Mathematics, 1971
- Semi-groups of nonlinear contractions and dissipative setsJournal of Functional Analysis, 1969
- Nonlinear semigroups and evolution equationsJournal of the Mathematical Society of Japan, 1967
- Functional Analysis and Semi-groups. (Revised Edition) By Einai Hille and Ralph S. Phillips. Pp. xii, 808. $13.80, 1957. Americaj Mathematical Society Colloquium Publications, Vol 31. (American Mathematical Society)The Mathematical Gazette, 1959