Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

• Autorzy: Jaroś J. , Takaśi K.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.l.47

• Języki publikacji: EN

Abstrakty

EN

We consider n-dimensional cyclic systems of second order differential equations [formula] (*) under the assumption that the positive constants α and β satisfy α1...αn > β1...βn and pi(t) and qi(t) are regularly varying functions, and analyze positive strongly increasing so­lutions of system (*) in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (*) can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (*) can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

Słowa kluczowe

EN

systems of differential equations; positive solutions; asymptotic behavior; regularly varying functions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 1
• Strony: 47--69
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Jaroś J.

• Comenius University Faculty of Mathematics, Physics and Informatics Department of Mathematical Analysis and Numerical Mathematics 842 48 Bratislava, Slovakia

autor

Takaśi K.

• Hiroshima University Faculty of Science Department of Mathematics Higashi-Hiroshima 739-8526, Japan

Bibliografia

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