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Remarks on the uniqueness of second order ODEs

Dalibor Pražák (2011)

Applications of Mathematics

We are concerned with the uniqueness problem for solutions to the second order ODE of the form x ' ' + f ( x , t ) = 0 , subject to appropriate initial conditions, under the sole assumption that f is non-decreasing with respect to x , for each t fixed. We show that there is non-uniqueness in general; on the other hand, several types of reasonable additional assumptions make the problem uniquely solvable. The interest in this problem comes, among other, from the study of oscillations of lumped parameter systems with implicit...

Renormalization of exponential sums and matrix cocycles

Alexander Fedotov, Frédéric Klopp (2004/2005)

Séminaire Équations aux dérivées partielles

In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics

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