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Tonti, E.

Variational formulation for every nonlinear problem. (English) Zbl 0558.49022

Int. J. Eng. Sci. 22, 1343-1371 (1984).
It is shown that for every linear or nonlinear problem, whose solution exists and is unique, one may find many functionals whose minimum is the solution of the problem. They are obtained after a transformation of the given problem into another by the application of an ”integrating operator”: this transforms a differential problem into an integro- differential one. The procedure used to obtain such functionals is straightforward and is described in detail. Examples are exhibited and the numerical effectiveness of the method is tested. The variational formulation so obtained contains the classical formulation as a particular case when it exists.

Cited in 1 Review
Cited in 46 Documents

MSC:

49Q99 Manifolds and measure-geometric topics
44A45 Classical operational calculus
58E30 Variational principles in infinite-dimensional spaces
47J05 Equations involving nonlinear operators (general)
47B25 Linear symmetric and selfadjoint operators (unbounded)
49S05 Variational principles of physics

Keywords:

transformation; integrating operator; variational formulation
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\textit{E. Tonti}, Int. J. Eng. Sci. 22, 1343--1371 (1984; Zbl 0558.49022)
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References:

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