Extremal solutions to a system of n nonlinear differential equations and regularly varying functions
| Authors | |
|---|---|
| Year of publication | 2015 |
| Type | Article in Periodical |
| Magazine / Source | Mathematische Nachrichten |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1002/mana.201400252 |
| Field | General mathematics |
| Keywords | Positive extremal solutions; asymptotic representation; quasilinear systems; Emden-Fowler systems; elliptic systems; regular variation |
| Description | 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. |
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