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., , . 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 .See , , , .
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. A survey of Gaetano Fichera's contributions to the theory of partial differential equations, written by two of his pupils. . . : for a review of the book, see . . The paper describes Fichera's approach toward 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 . . , reviewed also by , and by . . . An expository paper detailing the contributions of Gaetano Fichera and his school on the problem of numerical calculation of eigenvalues for general differential operators.