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Variational methods for solving nonlinear equations (differential, integral, etc.) are perhaps the most common methods at the present time. However, the history of their origin and development, both in the USSR and in the whole world, has not been studied enough. The author attempts to fill this gap, limiting himself mainly to 1920's-1950's, starting with Hilbert’s works on justification of Dirichlet...
The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within the framework of which Polish-Soviet interaction was most clearly manifested. In the period up to the mid-twentieth century these areas were advanced by the representatives of Lvov Mathematical School,...
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