Tonti, Enzo On the variational formulation for linear initial value problems. (English) Zbl 0278.49047 Ann. Mat. Pura Appl., IV. Ser. 95, 331-359 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 36 Documents MSC: 49R50 Variational methods for eigenvalues of operators (MSC2000) PDF BibTeX XML Cite \textit{E. Tonti}, Ann. Mat. Pura Appl. (4) 95, 331--359 (1973; Zbl 0278.49047) Full Text: DOI References: [1] M. M. Vainberg,Variational Methods in the Study of Nonlinear Operators, Holden Day, 1964. · Zbl 0122.35501 [2] Tonti, E., Variational formulation of nonlinear differential equations, Bull. Acad. Roy. Belgique, 5^serie, IV, 137-165 (1969) · Zbl 0182.11402 [3] E. Tonti,On the Inverse Problem of the Calculus of Variations, Academic Press (in press). · Zbl 0503.35008 [4] P. M. Morse -H. Feshbach,Methods of Theoretical Physics, vol. I, McGraw-Hill, 1953. · Zbl 0051.40603 [5] C. Lanczos,Linear Differential Operators, Van Nostrand, 1961. · Zbl 0111.08305 [6] M. Becker,The Principles and Applications of Variational Methods, M.I.T. Press, 1964. · Zbl 0132.34203 [7] J. Lewins,Importance. The Adjoint Function, Pergamon Press, 1965. [8] Nichols, R. A.; Bankoff, S. G., Adjoint variational principles for convective diffusion, Int. J. Heat Mass Transfer, 8, 329-335 (1963) · Zbl 0133.21201 [9] Stattery, I. C., A widely applicable type of variational integral, Chem. Engr. Sci., 19, 801-801 (1964) [10] Gurtin, M. E., Variational principles for linear initial value problems, Quart. Appl. Math., 22, 252-256 (1964) · Zbl 0173.37602 [11] Gurtin, M. E., Variational principles for linear elastodynamics, Arch. Rat. Mech., 34, 16-16 (1964) · Zbl 0124.40001 [12] Gurtin, M. E., Variational principles in the linear theory of viscoelasticity, Arch. Rat. Mech. Anal., 13, 3, 179-191 (1963) · Zbl 0123.40803 [13] Tao, L. N., On variational principles for electromagnetic theory, Jour. Math. Phys., 7, 526-526 (1966) · JFM 57.0490.07 [14] I. Hlavacek,Variational principles for parabolic equations, Aplikace Mathematiky, Ceskoslovenska Akademie Ved,14 (1969). · Zbl 0182.13803 [15] Sandhu, R. S.; Pister, K. S., A variational principle for linear, coupled field problems in continuum mechanics, Int. J. Engin. Sci., 8, 989-999 (1970) · Zbl 0215.28701 [16] Sandhu, R. S.; Pister, K. S., Variational principles for boundary value and initial-boundary value problems in continuum mechanics, Int. J. Solid. Structures, 7, 639-654 (1971) · Zbl 0228.73014 [17] Bourbaki, N., Eléments de mathematique, Livre V, Espaces vectoriels topologiques (1966), Paris: Hermann, Paris · Zbl 0139.24602 [18] J. J. Moreau,Fonctionnelles convexes, Séminaire sur les équations aux dérivées partielles, Collège de France (1966-67) (policopy). [19] J. J. Moreau,Convexity and duality, in Functional analysis and optimization, Academic Press, 1966. [20] N. I. Akiezer -I. M. Glazman,Theory of linear operators in Hilbert space, vol. I, Ungar Publ. Co., 1961. [21] S. G. Mikhlin,Variational Methods in Mathematical Physics, Pergamon Press, 1964. · Zbl 0119.19002 [22] Hlavacek, I., On the existence and uniquencess of solution of the Cauchy problem for linear integro-differential equations with operator coefficients, Apl. Matematiky, 16, 64-64 (1971) · Zbl 0217.15801 [23] Goodman, T. R., The adjoint heat-conduction problem for solids, Proc. fourth U.S. Nat. Congr. Appl. Mech., II, 1257-1257 (1962) · Zbl 0825.62129 [24] R. S. Schechter,The Variational Method in Engineering, McGraw-Hill, 1967. · Zbl 0176.10001 [25] H. L. Dryden -F. P. Murnaghan -H. Bateman,Hydrodynamics, Dover, 1956, p. 167. · Zbl 0071.40102 [26] Coleman, B. D., Thermodynamics of material with memory, Arch. Rat. Mech. Anal., 17, 1-1 (1964) [27] Pontryagin, L. S., Hermitean operators in a space with indefinite metric, Izv. Akad. Nauk. SSSR, Ser. Mat., 8, 6, 243-280 (1944) · Zbl 0061.26004 [28] Nevanlinna, R., Ann. Ac. Sci. Fenn., 1, 108-108 (1953) [29] Pandit, L. K., Linear vector spaces with indefinite metric, Nuovo Cimento, serie X, 11, 157-157 (1958) · Zbl 0119.31804 [30] N. Dunford -J. T. Schwartz,Linear Operators, Part. II, Interscience, 1963. [31] Levoni, S., Variational principles in the electrostatics of hereditary media, Meccanica, 6, 3-3 (1971) 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.