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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

1999

tom 72

nr 2

181-190

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.

On solutions of third order nonlinear differential equations

88%

Mojsej I., Ohriska J.

Open Mathematics

2006

tom 4

nr 1

46-63

The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with deviating argument. In particular, we prove a comparison theorem for properties A and B as well as a comparison result on property A between nonlinear equations with and without deviating arguments. Our assumptions on nonlinearity f are related to its behavior only in a neighbourhood of zero and/or of infinity.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Open Mathematics

1 Augustynowicz A.

1 Mojsej I.

1 Ohriska J.

1 2006

1 1999

Wyniki wyszukiwania

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

On solutions of third order nonlinear differential equations