Extremal solutions to a system of n nonlinear differential equations and regularly varying functions

0445822 - MÚ 2016 RIV DE eng J - Článek v odborném periodiku
Matucci, S. - Řehák, Pavel
Extremal solutions to a system of n nonlinear differential equations and regularly varying functions.
Mathematische Nachrichten. Roč. 288, 11-12 (2015), s. 1413-1430. ISSN 0025-584X. E-ISSN 1522-2616
Grant ostatní: GA ČR(CZ) GAP201/10/1032
Program: GA
Institucionální podpora: RVO:67985840
Klíčová slova: positive extremal solutions * asymptotic representation * quasilinear systems
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.688, rok: 2015
http://onlinelibrary.wiley.com/doi/10.1002/mana.201400252/abstract

The strongly increasing and strongly decreasing solutions to a system of n nonlinear first order equations are here studied, under the assumption that both the coefficients and the nonlinearities are regularly varying functions. We establish conditions under which such solutions exist and are (all) regularly varying functions, we derive their index of regular variation and establish asymptotic representations. Several applications of the main results are given, involving n-th order nonlinear differential equations, equations with a generalized Laplacian, and nonlinear partial differential systems.
Trvalý link: http://hdl.handle.net/11104/0247888