Travis, C. C.; Webb, G. F. Existence and stability for partial functional differential equations. (English) Zbl 0299.35085 Trans. Am. Math. Soc. 200, 395-418 (1974). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 282 Documents MSC: 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B35 Stability in context of PDEs 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) × Cite Format Result Cite Review PDF Full Text: DOI References: [1] H. Brézis and A. Pazy, Convergence and approximation of semigroups of nonlinear operators in Banach spaces, J. Functional Analysis 9 (1972), 63 – 74. · Zbl 0231.47036 [2] Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York Inc., New York, 1967. · Zbl 0164.43702 [3] M. G. Crandall and T. M. Liggett, Generation of semi-groups of nonlinear transformations on general Banach spaces, Amer. J. Math. 93 (1971), 265 – 298. · Zbl 0226.47038 · doi:10.2307/2373376 [4] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402 [5] Jack K. Hale, Linear functional-differential equations with constant coefficients, Contributions to Differential Equations 2 (1963), 291 – 317 (1963). [6] Jack K. Hale, Functional differential equations, Springer-Verlag New York, New York-Heidelberg, 1971. Applied Mathematical Sciences, Vol. 3. · Zbl 0222.34063 [7] Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. · Zbl 0078.10004 [8] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. · Zbl 0148.12601 [9] A. Pazy, On the differentiability and compactness of semigroups of linear operators, J. Math. Mech. 17 (1968), 1131 – 1141. · Zbl 0162.45903 [10] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. · Zbl 0121.05501 [11] Irving Segal, Non-linear semi-groups, Ann. of Math. (2) 78 (1963), 339 – 364. · Zbl 0204.16004 · doi:10.2307/1970347 [12] Angus E. Taylor, Introduction to functional analysis, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. · Zbl 0081.10202 [13] G. F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1 – 12. · Zbl 0277.34070 · doi:10.1016/0022-247X(74)90277-7 [14] Kôsaku Yosida, Functional analysis, Second edition. Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York Inc., New York, 1968. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.