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Some remarks on comparison functions

100%

Augustynowicz A.

Annales Polonici Mathematici

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2009

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tom 96

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nr 2

97-106

EN

We answer some questions concerning Perron and Kamke comparison functions satisfying the Carathéodory condition. In particular, we show that a Perron function multiplied by a constant may not be a Perron function, and that not every comparison function is bounded by a comparison function with separated variables. Moreover, we investigate when a sum of Perron functions is a Perron function. We also present a criterion for comparison functions with separated variables.

2

On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments

100%

Augustynowicz A.

Annales Polonici Mathematici

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1999

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tom 72

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nr 2

181-190

EN

We prove an existence theorem of Cauchy-Kovalevskaya type for the equation $D_t u(t,z) = f(t,z,u(α^{(0)}(t,z)), D_z u(α^{(1)}(t,z)),...,D_z^k u(α^{(k)}(t,z)))$ where f is a polynomial with respect to the last k variables.

3

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On extremal solutions of differential equations with advanced argument

63%

Augustynowicz A., Jankowski J.

Commentationes Mathematicae

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2006

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tom 46

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nr 1

EN

We obtain existence of absolutely continuous extremal solutions of the problem $u'(x) = F(x, u(x), u(h(x)))$, $u(0) = u_0$, and the Darboux problem for $u_{xy}(x, y) = G(x, y, u(x, y), u(H(x, y)))$, where $h$ and $H$ are arbitrary continuous deviated arguments.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Commentationes Mathematicae

3 Augustynowicz A.

1 Jankowski J.

1 2009

1 2006

1 1999

Some remarks on comparison functions

On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments

On extremal solutions of differential equations with advanced argument