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Caratheodory's solution of the Cauchy problem and a question of Z. Grande

In: Mathematica Slovaca, vol. 68, no. 6
Volodymyr Mykhaylyuk - Vadym Myronyk
Detaily:
Rok, strany: 2018, 1367 - 1372
Kľúčové slová:
Caratheodory's solution, quasicontinuity, semicontinuity, $sup$-measurability
O článku:
It is shown that for a function $f\:[a,b]\times\mathbb{R}\to \mathbb{R}$ which is measurable with respect to the first variable and upper semicontinuous quasicontinuous and increasing with respect to the second variable there exists a Caratheodory's solution $y(x)=y_0+\int\limits_{x_0}^xf(t,y(t))\dd\mu(t)$ of the Cauchy problem $y'(x)=f(x,y(x))$ with the initial condition $y(x_0)=y_0$. There is constructed an example which indicate to essentiality of condition of increasing and give the negative answer to a question of Z. Grande.
Ako citovať:
ISO 690:
Mykhaylyuk, V., Myronyk, V. 2018. Caratheodory's solution of the Cauchy problem and a question of Z. Grande. In Mathematica Slovaca, vol. 68, no.6, pp. 1367-1372. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0187

APA:
Mykhaylyuk, V., Myronyk, V. (2018). Caratheodory's solution of the Cauchy problem and a question of Z. Grande. Mathematica Slovaca, 68(6), 1367-1372. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0187
O vydaní:
Publikované: 3. 12. 2018