Fichera's existence principle explained

In mathematics, and particularly in functional analysis, Fichera's existence principle is an existence and uniqueness theorem for solution of functional equations, proved by Gaetano Fichera in 1954.^[1] More precisely, given a general vector space and two linear maps from it onto two Banach spaces, the principle states necessary and sufficient conditions for a linear transformation between the two dual Banach spaces to be invertible for every vector in .^[2]

References

• . A survey of Gaetano Fichera's contributions to the theory of partial differential equations, written by two of his pupils.
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for a review of the book, see .

• . The paper Some recent developments of the theory of boundary value problems for linear partial differential equations describes Fichera's approach to a general theory of boundary value problems for linear partial differential equations through a theorem similar in spirit to the Lax–Milgram theorem.
• . A monograph based on lecture notes, taken by Lucilla Bassotti and Luciano De Vito of a course held by Gaetano Fichera at the INdAM: for a review of the book, see .
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• , reviewed also by, and by
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• . An expository paper detailing the contributions of Gaetano Fichera and his school on the problem of numerical calculation of eigenvalues for general differential operators.

Notes and References

1. ,, .
2. See,,, .