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Book Review

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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.

References [Enhancements On Off] (What's this?)

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  • 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.

Review Information:

Reviewer: Roman I. Andrushkiw
Journal: Bull. Amer. Math. Soc. 25 (1991), 221-228
DOI: https://doi.org/10.1090/S0273-0979-1991-16073-8
American Mathematical Society