Asymptotic Solutions of nth Order Dynamic Equation and Oscillations
نویسندگان
چکیده
منابع مشابه
Asymptotic Solutions of nth Order Dynamic Equation and Oscillations
We establish a new asymptotic theorem for the nth order nonautonomous dynamic equation by its transformation to the almost diagonal system and applying Levinson’s asymptotic theorem.Our transformation is given in the terms of unknown phase functions and is chosen in such a way that the entries of the perturbation matrix are the weighted characteristic functions. The characteristic function is d...
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where n >, 2, a: [0, 00) + [0, a~), q: [0, co) --+ (-00, co), andf: (--co, 03) + (-00, CQ). We assume a(l), q(t), andf( x are continuous, q(t) < t for all t > 0, q(t) 3 co ) as t ---f co, and xf(x) > 0 for x # 0. Usually, a condition of monotonicity on f is needed in order to obtain results for Eq. (1) analogous to those of an ordinary differential equation of the same type. Many authors observ...
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ژورنال
عنوان ژورنال: ISRN Mathematical Analysis
سال: 2013
ISSN: 2090-4665
DOI: 10.1155/2013/946453