Can we say something about solutions of the second order differential equations of the form:
f′′+q(z)f′+p(z)f=0
where p and q are rational functions such that q(z)→0, z→∞
Cher Zinelaabidine,
Pouvez-vous regarder l'article ci-joint de F.Klein et me dire si la condition imposée dans votre question peut nous donner une sous classe qui a un intérêt concret et étudier les singularités de l'équation qui proviennent des fonctions q(z) et p(z).
Cordialement
Abdelkader Intissar
Solution is in the form of C+Dexp(-mt) where C, D are any constants and m is the root of the auxiliary equation. As per your question, 'm' must be m>0. Solution will have a bias term of C. Then final value is C where as it starts from C+D.
Dear Professor Abdelkader;
The equation :
[eta]=P
in the paper of F.Klein seems to be helpful in the way we can give an upper bound for the degree of the rational function p(z) (since q(z)→0 ).
Dear Jagannath ;
Thank you for your interest, but it seems to me that you consider only the case when the coefficients are constants.
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