Nonoscillatory Solutions of Second-Order Superlinear Dynamic Equations with Integrable Coefficients
نویسندگان
چکیده
منابع مشابه
Nonoscillatory Solutions of Second Order Differential Equations with Integrable Coefficients
The asymptotic behavior of nonoscillatory solutions of the equation x" + a{t)\x\' sgnx = 0, y > 0 , is discussed under the condition that A(t) = limr_00/, a(s)ds exists and A(t) > 0 for all t. For the sublinear case of 0 < y < 1 , the existence of at least one nonoscillatory solution is completely characterized.
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where a(t) is a locally integrable function of /. We call equation (1) oscillatory if all solutions of (1) have arbitrarily large zeros on [0, oo), otherwise, we say equation (1) is nonoscillatory. As a consequence of Sturm's Separation Theorem [21], if one of the solutions of (1) is oscillatory, then all of them are. The same is true for the nonoscillation of (1). The literature on second orde...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2012
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2012/812165