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Poincaré’s early use of Analysis situs in nonlinear differential equation : variations around the theme of Kronecker’s integral

Jean Mawhin — 2000

Philosophia Scientiae

We analyze the chronological and conceptual evolution of the early use by Poincaré of tools, and in particular of in his qualitative theory of nonlinear differential equations. We show in this way that prior to his famous series of subsequent papers on Poincaré had already obtained or anticipated many important topological results.

Nonlinear boundary value problems involving the extrinsic mean curvature operator

Jean Mawhin — 2014

Mathematica Bohemica

The paper surveys recent results obtained for the existence and multiplicity of radial solutions of Dirichlet problems of the type · v 1 - | v | 2 = f ( | x | , v ) in B R , u = 0 on B R , where B R is the open ball of center 0 and radius R in n , and f is continuous. Comparison is made with similar results for the Laplacian. Topological and variational methods are used and the case of positive solutions is emphasized. The paper ends with the case of a general domain.

A tribute to Juliusz Schauder

Jean Mawhin — 2018

Antiquitates Mathematicae

An analysis of the mathematical contributions of Juliusz Schauder through the writings of contemporary mathematicians, and in particular Leray, Hadamard, Banach, Randolph, Federer, Lorentz, Ladyzhenskaya, Ural’tseva, Orlicz, Gårding and Pietsch.

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