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Displaying similar documents to “An abstract non-linear Cauchy-Kowalewski theorem and its proof by a contraction-mapping principle”

Abstract version of the Cauchy-Kowalewski problem

Oleg Zubelevich (2004)

Open Mathematics

Similarity:

We consider an abstract version of the Cauchy-Kowalewski Problem with the right hand side being free from the Lipschitz type conditions and prove the existence theorem.

On the Cauchy problem for linear PDEs with retarded arguments at derivatives

Krzysztof A. Topolski (2015)

Annales Polonici Mathematici

Similarity:

We present an existence theorem for the Cauchy problem related to linear partial differential-functional equations of an arbitrary order. The equations considered include the cases of retarded and deviated arguments at the derivatives of the unknown function. In the proof we use Tonelli's constructive method. We also give uniqueness criteria valid in a wide class of admissible functions. We present a set of examples to illustrate the theory.