On singular solutions of a second order differential equation
نویسندگان
چکیده
منابع مشابه
On Singular Solutions of a Second Order Differential Equation
In the paper, sufficient conditions are given under which all nontrivial solutions of (g(a(t)y))+r(t)f(y) = 0 are proper where a > 0, r > 0, f(x)x > 0, g(x)x > 0 for x 6= 0 and g is increasing on R. A sufficient condition for the existence of a singular solution of the second kind is given.
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for values of x > 0. For values of x < 0, if r is an integer then one can employ the solution given by eq. (2) without modification. If r is not an integer, then one can obtain the solution from eq. (2) by analytic continuation in the complex plane. In particular, for non-integer r there is a branch point at x = 0 and it is convenient to choose the branch cut to lie along the negative real axis...
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2006
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2006.1.8