کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4631605 | 1340625 | 2011 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Fractal oscillations of self-adjoint and damped linear differential equations of second-order
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
For a prescribed real number s â [1, 2), we give some sufficient conditions on the coefficients p(x) and q(x) such that every solution y = y(x), y â C2((0, T]) of the linear differential equation (p(x)yâ²)â²Â + q(x)y = 0 on (0, T], is bounded and fractal oscillatory near x = 0 with the fractal dimension equal to s. This means that y oscillates near x = 0 and the fractal (box-counting) dimension of the graph Î(y) of y is equal to s as well as the s dimensional upper Minkowski content (generalized length) of Î(y) is finite and strictly positive. It verifies that y admits similar kind of the fractal geometric asymptotic behaviour near x = 0 like the chirp function ych(x) = a(x)S(Ï(x)), which often occurs in the time-frequency analysis and its various applications. Furthermore, this kind of oscillations is established for the Bessel, chirp and other types of damped linear differential equations given in the form yâ³Â + (μ/x)yâ²Â + g(x)y = 0, x â (0, T]. In order to prove the main results, we state a new criterion for fractal oscillations near x = 0 of real continuous functions which essentially improves related one presented in [1].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 5, 1 November 2011, Pages 2281-2293
Journal: Applied Mathematics and Computation - Volume 218, Issue 5, 1 November 2011, Pages 2281-2293
نویسندگان
Mervan PaÅ¡iÄ, Satoshi Tanaka,