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The direct variational method for operator equations \(u^ k+C^ mu=f, k=1,2; m\in N\). (Russian) Zbl 0826.34063
Summary: The approach of S. E. Zhelezovskij, V. V. Kirichenko and V. A. Krys’ko [Differ. Uravn. 25, No. 4, 652-659 (1989; Zbl 0688.35049)] to the construction of symmetrizing operators for hyperbolic partial differential equations is extended to some other operator equations, among which the case of a parabolic equation is of particular interest. On the basis of this approach, a direct variational method for the solution of the considered equations is constructed.
34G20 Nonlinear differential equations in abstract spaces
35K15 Initial value problems for second-order parabolic equations
35L15 Initial value problems for second-order hyperbolic equations
49R50 Variational methods for eigenvalues of operators (MSC2000)