Bulletin of the American Mathematical Society

MathSciNet review: 1567949
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Book Information:

Author: V. M. Filippov
Title: Variational principles for nonpotential operators
Additional book information: Transl. Math. Monographs, vol. 77, Amer. Math. Soc. Providence, RI, 1989, 239 pp., $99.00. ISBN 0-8218-4529-2.

F. Balatoni, Über die Charakterisierbarkeit partieller Differentialgleichungen zweiter Ordnung mit Hilfe der Variationsrechnung, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 229–233 (German, with Russian summary). MR 132423

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E. T. Copson, Partial differential equations and the calculus of variations, Proc. Roy. Soc. Edinburgh 46 (1925/26), 126-135.

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K. O. Friedrichs, Ein Verfahren der Variationsrechnung das Minimum eines Integrals als das Maximum eines anderen Ausdruckes darzustellen, Nachr. Ges. Wiss. Göttingen Math. -Phys. Kl. (1929), 13-20.

K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55 (1944), 132–151. MR 9701, DOI 10.1090/S0002-9947-1944-0009701-0

David Hilbert, Über das Dirichletsche Prinzip, Math. Ann. 59 (1904), no. 1-2, 161–186 (German). MR 1511266, DOI 10.1007/BF01444753

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B. Levi, Sul principo di Dirichlet, Rend. Circ. Mat. Palermo 6 (1906), 293-360.

W. V. Petryshyn, On the extension and the solution of nonlinear operator equations, Illinois J. Math. 10 (1966), 255–274. MR 208432

W. V. Petryshyn, Direct and iterative methods for the solution of linear operator equations in Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 136–175. MR 145651, DOI 10.1090/S0002-9947-1962-0145651-8

V. M. Šalov, Minimum principle of a quadratic functional for a hyperbolic equation, Differencial′nye Uravnenija 1 (1965), 1338–1365 (Russian). MR 0186950

V. M. Šalov, A certain generalization of the space of K. Friedrichs, Dokl. Akad. Nauk SSSR 151 (1963), 292–294 (Russian). MR 0150596

M. G. Slobodyanskiĭ, On transformation of the problem of the minimum of a functional to the problem of the maximum, Dokl. Akad. Nauk SSSR (N.S.) 91 (1953), 733–736 (Russian). MR 0071869

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S. Zaremba, Sur le principe de minimum, Bull. Int. Acad. Sci. Cracovie Cl. Sci. Math. Nat. 7 (1909), 199-264.

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F. Belatoni, Über die Charakterisierbarkeit partieller Differentialgleichungen zweiter Ordnung mit Hilfe der Variationsrechnung, Magyar Tud. Akad. Mat. Kutató Int. Közl. 5 (1960), 229-233. MR 0132423

2.

E. T. Copson, Partial differential equations and the calculus of variations, Proc. Roy. Soc. Edinburgh 46 (1925/26), 126-135.

3.

K. O. Friedrichs, Ein Verfahren der Variationsrechnung das Minimum eines Integrals als das Maximum eines anderen Ausdruckes darzustellen, Nachr. Ges. Wiss. Göttingen Math. -Phys. Kl. (1929), 13-20.

4.

K. O. Friedrichs, The identity of weak and strong extensions of differential operators, Trans. Amer. Math. Soc. 55 (1944), 132-151. MR 9701

5.

D. Hilbert, Über das Dirichletsche Prinzip, Math. Ann. 59 (1904), 161-186. MR 1511266

6.

B. Levi, Sul principo di Dirichlet, Rend. Circ. Mat. Palermo 6 (1906), 293-360.

7.

W. V. Petryshyn, On the extension and the solution of nonlinear operator equations, Illinois J. Math. 10 (1966), 255-274. MR 208432

8.

W. V. Petryshyn, Direct and iterative methods for the solution of linear operator equations in Hilbert space, Trans. Amer. Math. Soc. 105 (1962), 675-690. MR 145651

9.

V. M. Shalov, The principle of a minimum of a quadratic functional for a hyperbolic equation, Differentsial'nye Uravneniya 1 (1965), 1338-1365; English transl, in Differential Equations 1 (1965). MR 186950

10.

V. M. Shalov, Solution of nonselfadjoint equations by the variational method, Dokl. Akad. Nauk SSSR 151 (1963), 511-512; English transl, in Soviet Math., Dokl. 4 (1963). MR 150597

11.

M. G. Slobodyanskii, On transformation of the problem of the minimum of a functional to the problem of the maximum, Dokl. Akad. Nauk SSSR 91(1953), 733-736. MR 71869

12.

S. Zaremba, Sur le principe de minimum, Bull. Int. Acad. Sci. Cracovie Cl. Sci. Math. Nat. 7 (1909), 199-264.