On solutions to a class of quasilinear differential systems with slowly varying parameters (Q2740273)
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scientific article; zbMATH DE number 1646613
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On solutions to a class of quasilinear differential systems with slowly varying parameters |
scientific article; zbMATH DE number 1646613 |
Statements
16 September 2001
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quasilinear differential system
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slowly varying functions
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particular solution
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critical case
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On solutions to a class of quasilinear differential systems with slowly varying parameters (English)
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The author announces his developments of results presented in the papers of \textit{A. V. Kostin} and \textit{S. A. Shchegolev} [Ukr. Mat. Zh. 41, No. 1, 101-103 (1989; Zbl 0701.34021); ibid. 50, No. 5, 654-664 (1998; Zbl 0914.34045)], and \textit{S. A. Shchegolev} [ibid. 51, No. 2, 285-288 (1999; Zbl 0937.34033)] in which the classes \(S_m, B_m\) of slowly varying functions were defined and the existence of solutions to the class \(B_{m-2}\) for systems with slowly varying coefficients were established. NEWLINENEWLINENEWLINENow the author generalizes these results to the case where the matrix of the linear part of \((2m+n)\)-dimensional quasilinear systems has \(m\) pairs of purely imaginary eigenvalues, while the real parts of the other eigenvalues are separated from zero.
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