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Global Existence Theorems for Solutions of Nonlinear Differential Equations with Prescribed Asymptotic Behaviour
Author(s) -
Kusano Takaši,
Trench William F.
Publication year - 1985
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-31.3.478
Subject(s) - nonlinear system , convergence (economics) , mathematics , interval (graph theory) , differential equation , differential (mechanical device) , mathematical analysis , physics , combinatorics , economics , quantum mechanics , thermodynamics , economic growth
Most known conditions implying that a nonlinear differential equation y ( n ) + f(t, y) = 0 has solutions such that lim t →∞ t − k y ( i ) = c ≠ 0 are local in that the solutions are guaranteed to exist only for sufficiently large t . This paper presents conditions ensuring that the solutions exist on a given interval and have the prescribed asymptotic behaviour. Some of the integral smallness conditions on f permit conditional convergence.