Exceptional solutions of n-th order periodic linear differential equations
نویسندگان
چکیده
منابع مشابه
Approximately $n$-order linear differential equations
We prove the generalized Hyers--Ulam stability of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.
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where n is a positive integer, s ≤ n − 1 a positive integer, bi(i = 1, · · · , s) are constants and k > 1 is an integer, f ∈ C(R,R) for ∀x ∈ R, p ∈ C(R,R) with p(t+ T ) = p(t). In recent years, some researchers used the coincidence degree theory of Mawhin to study the existence of periodic solutions of first, second or third order differential equations [5, 6], [9][15]–[19], [22, 23], [25, 26]....
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we prove the generalized hyers--ulam stability of n--th order linear differential equation of the form $y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x)$, with condition that there exists a non--zero solution of corresponding homogeneous equation. our main results extend and improve the corresponding results obtained by many authors.
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ژورنال
عنوان ژورنال: Complex Variables, Theory and Application: An International Journal
سال: 1997
ISSN: 0278-1077,1563-5066
DOI: 10.1080/17476939708815033