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Functional analysis and nonlinear boundary value problems: the legacy of Andrzej Lasota. (English) Zbl 1326.34013

From the text: The main features of Lasota’s papers on the functional analysis approach to boundary value problems are characterized by a careful choice of underlying function spaces to obtain maximal generality, an abunant use of Schauder’s linearization followed by Schauder’s fixed point theorem, an elegant use of various types of inequalities, a special care for getting sharp existence and/or uniqueness conditions, and a clever use of differential inclusions to state existence conditions for differential equations.
Other results of Lasota on boundary value problems are based upon shooting method, Pontryagin’s maximum principle, Brouwer’s invariance of domain theorem, and Wazeski’s method.
Lasota’s contributions to the methods of functional analysis in nonlinear boundary value problems impress by their originality, number and elegance. They fully belong to the rich functional analytic and topological tradition of the Polish mathematical school. They have inspired many further contributions in Poland and abroad, and will continue to do so. They reflect the nice personality of their author.

MSC:

34-03 History of ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
01A70 Biographies, obituaries, personalia, bibliographies
34B15 Nonlinear boundary value problems for ordinary differential equations
47H10 Fixed-point theorems

Biographic References:

Lasota, Andrzej
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