Abstract
We consider the operator equation
.
It came as a complete surprise, when, in a short note published in 1900, Fredholm showed that the general theory of all integral equations considered prior to him was, in fact, extremely simple.
Ivar Fredholm (1866–1927) was a student of Mittag-Leffler in Stockholm in 1888–1890; he published only a few papers during his lifetime, mostly concerned with partial differential equations. After a visit to Paris, where he had been in contact with all the French analysts, and had become familiar with the recent papers of Poincaré, he communicated, in August 1899, his first results on integral equations to his former teacher; they were published in 1900 and completed two years later in a paper published in Acta Mathematica.
Jean Dieudonné (1981)
The purpose of this note is to introduce a nonlinear version of Fredholm operators, and to prove that in this context Sard’s theorem (1942) holds if zero measure is replaced by first category.
Steve Smale (1965)
These notes formed the basis of a course entitled “Nonlinear Problems” given at the Department of Mathematical Analysis, Charles University, Prague, during the years 1976 and 1977.
The problems of solvability of noncoercive nonlinear equations and of nonlinear Fredholm alternatives have been very popular recently. Therefore, it was the author’s desire to give a survey of results concerning these problems which are known at present, as well as to show the methods which have been used to obtain them and some of their consequences for concrete problems.
Svatopluk Fučik (1977)
Svatopluk Fučik died prematurely on May 18,1979. He was 34 years old and knew since 1973 that his time was severely limited. 1973 is also the year when Fučik wrote the first of twenty-one papers devoted to nonlinear noncoercive problems.... This domain of analysis owes so much to his remarkable ingenuity and formidable energy.
Jean Mawhin(1981)
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Zeidler, E. (1990). Noncoercive Equations, Nonlinear Fredholm Alternatives, Locally Monotone Operators, Stability, and Bifurcation. In: Nonlinear Functional Analysis and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0981-2_5
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