Asymptotically constant functions and second order linear oscillation
نویسندگان
چکیده
منابع مشابه
Integral Criteria for Second-Order Linear Oscillation
We present several new criteria for the oscillation of the second-order linear equation y(t) + q(t)y(t) = 0, in which the coefficient q may or may not change signs. The criteria involve the integral ∫ tq(t) dt for some γ > 0. The special case γ = 2 is then studied in greater details. AMS Subject Classification: 34C10
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where p(x) is a continuous positive function for 0<x< oo. Equation (1) is said to be nonoscillatory in (a, oo) if no solution of (1) vanishes more than once in this interval. Because of the Sturm separation theorem, this is equivalent to the existence of a solution which does not vanish at all in (a, oo). The equation will be called nonoscillatory—without the interval being mentioned —if there ...
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A non-trivial solution of (1) is called oscillatory if for every N > 0 there exists an n > N such that X,X n + , 6 0. If one non-trivial solution of (1) is oscillatory then, by virtue of Sturm’s separation theorem for difference equations (see, e.g., [S]), all non-trivial solutions are oscillatory, so, in studying the question of whether a solution {x,> of (1) is oscillatory, it is no restricti...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1983
ISSN: 0022-247X
DOI: 10.1016/0022-247x(83)90188-9