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Extremal solutions to a system of n nonlinear differential equations and regularly varying functions
Author(s) -
Matucci Serena,
Řehák Pavel
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400252
Subject(s) - mathematics , nonlinear system , differential equation , mathematical analysis , order (exchange) , laplace operator , physics , finance , quantum mechanics , economics
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 ϕ‐Laplacian, and nonlinear partial differential systems.