Abstract
Complementary (upper and lower) bivariational bounds are presented on the inner product 〈g,φ〉 associated with the solution φ of an arbitrary non-linear problem Fφ=0 in a real Hilbert space H. They take the form J(Ψ, Φ)±C(Ψ, Φ), where C(Ψ, Φ) is a positive bivariational approximation to zero and
is a bivariational approximation to 〈g,φ〉. The applicability of the bounds is briefly discussed.
The authors would like to acknowledge support from the Science Research Council.
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References
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© 1976 Springer-Verlag
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Barnsley, M.F., Robinson, P.D. (1976). Bivariational bounds on 〈g,φ〉 for non-linear problems Fφ=O. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087323
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DOI: https://doi.org/10.1007/BFb0087323
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