Seventy-five years of global analysis around the forced pendulum equation
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.
We prove an Ambrosetti–Prodi type result for the periodic solutions of the equation , when is arbitrary and or when . The proof uses upper and lower solutions and the Leray–Schauder degree.
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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