On the asymptotic behavior of solutions of a nonlinear equation
1964; American Mathematical Society; Volume: 15; Issue: 6 Linguagem: Inglês
10.1090/s0002-9939-1964-0176170-8
ISSN1088-6826
Autores Tópico(s)Functional Equations Stability Results
ResumoThis theorem is an extension of a theorem of Atkinson [21. Theorem 1 of this paper establishes the sufficiency of the above theorem without an assumption as to the sign of a(t). A theorem somewhat like the theorem of Trench [3] is given in Theorem 2 but for a nonlinear equation. As an application of this theorem, a stronger asymptotic result (under a stronger assumption) for equation (1) is given in Theorem 3. Other theorems on the asymptotic behavior of (1) when a(t) > 0 are contained in [4 ]. THEOREM 1. If a(t) is continuous and
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