Travis, C. C.; Webb, G. F. Cosine families and abstract nonlinear second order differential equations. (English) Zbl 0388.34039 Acta Math. Acad. Sci. Hung. 32, 75-96 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 228 Documents MSC: 34G20 Nonlinear differential equations in abstract spaces 47D03 Groups and semigroups of linear operators 47J05 Equations involving nonlinear operators (general) PDF BibTeX XML Cite \textit{C. C. Travis} and \textit{G. F. Webb}, Acta Math. Acad. Sci. Hung. 32, 75--96 (1978; Zbl 0388.34039) Full Text: DOI References: [1] V. Barbu, A class of boundary problems for second order abstract differential equations,J. Fac. Sci. Univ. Tokyo I A Math.,19 (1972), 295–319. · Zbl 0256.47052 [2] V. Barbu,Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International (Leyden. The Netherlands, 1975). [3] G. Da Prato andE. Giusti, Una caratterizzazione dei generatori di funzioni coseno astratte,Boll. Unione Mat. Italiana. 22 (1967), 357–362. · Zbl 0186.47702 [4] N. Dunford andJ. T. Schwartz,Linear Operators, Part I: General Theory, Interscience (New York, 1958). · Zbl 0084.10402 [5] H. O. Fattorini, Ordinary differential equations in linear topological spaces, I,J. Differential Equations,5 (1968), 72–105. · Zbl 0175.15101 [6] H. O. Fattorini, Ordinary differential equations in linear topological spaces, II,J. Differential Equations,6 (1969), 50–70. · Zbl 0181.42801 [7] H. O. Fattorini, Uniformly bounded cosine functions in Hilbert space,Indiana Univ. Math. J.,20 (1970), 411–425. · Zbl 0185.38501 [8] E. Giusti, Funzioni coseno periodiche,Boll. Unione Mat. Italiana,22 (1967), 478–485. · Zbl 0182.19304 [9] J. Goldstein, Semi-groups and hyperbolic equations,J. Functional Analysis,4 (1969), 50–70. · Zbl 0179.14605 [10] J. Goldstein, On a connection between first and second order differential equations in Banach spaces.J. Math. Anal. Appl.,30 (1970), 246–251. · Zbl 0197.12106 [11] J. Goldstein, On the convergence and approximation of cosine functions,Aequationes Math.,11 (1974), 201–205. · Zbl 0282.47012 [12] J. Goldstein,Semigroups of Operators and Abstract Cauchy Problems, Monograph, Tulane University (New Orleans, 1970). · Zbl 0219.47037 [13] T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag (New York, 1966). · Zbl 0148.12601 [14] J. Kisyński, On operator-valued solutions of d’Alembert’s functional equation, I,Colloquium Math.,23 (1971), 107–114. [15] Y. Konishi, Cosine functions of operators in locally convex spaces,J. Fac. Sci. Univ. Tokyo I. A. Math.,18 (1971/72), 443–463. · Zbl 0239.47034 [16] S. G. Krein,Lienar Differential Equations in Banach Spaces, Amer. Math. Soc. Translations of Math. Monographs, Vol.29 (Providence, 1971). [17] S. Kurepa, On some functional equations in Banach spaces,Studia Math.,19 (1960), 149–158. · Zbl 0100.32702 [18] S. Kurepa, A cosine funcational equation in Banach algebras,Acta Sci. Math. Szeged,23 (1962), 255–267. · Zbl 0113.31702 [19] V. Lakshmikantham,Differential Equations in Abstract Spaces, Academic Press (New York, 1972). · Zbl 0257.34002 [20] B. Nagy, On the generators of cosine operator functions,Publ. Math. Debrecen,21 (1974), 151–154. · Zbl 0314.47018 [21] B. Nagy, On cosine operator functions in Banach spaces,Acta Sci. Math. Szeged,36 (1974), 281–289. · Zbl 0273.47008 [22] B. Nagy, Cosine operator functions and the abstract Cauchy problem,Periodica Math. Hungar.,7(3) (1976), 15–18. · Zbl 0329.34051 [23] I. Segal, Non-linear semi-groups,Ann. Math.,78 (1963), 339–364. · Zbl 0204.16004 [24] M. Sova, Cosine operator functions,Rozprawy Matematiyczne,49 (1966), 1–47. · Zbl 0156.15404 [25] M. Sova, Semigroups and cosine functions of normal operators in Hilbert spaces,Časopis Pěst. Mat.,93 (1968), 437–458. · Zbl 0172.40606 [26] C. Travis andG. Webb, Existence and stability for partial functional differential equations,Trans. Amer. Math. Soc.,200 (1974), 395–418. · Zbl 0299.35085 [27] K. Yosida,Functional Analysis, Fourth Ed., Springer-Verlag (New York, 1974). · Zbl 0286.46002 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.