On Kneser solutions of higher order nonlinear ordinary differential equations |
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Authors: | Vladimir A Kozlov |
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Institution: | 1. Department of Mathematics, Link?ping University, SE-581 83, Link?ping, Sweden
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Abstract: | The equationx
(n)(t)=(−1)
n
│x(t)│
k
withk>1 is considered. In the casen≦4 it is proved that solutions defined in a neighbourhood of infinity coincide withC(t−t0)−n/(k−1), whereC is a constant depending only onn andk. In the general case such solutions are Kneser solutions and can be estimated from above and below by a constant times (t−t
0)−n/(k−1). It is shown that they do not necessarily coincide withC(t−t0)−n/(k−1). This gives a negative answer to two conjectures posed by Kiguradze that Kneser solutions are determined by their value in
a point and that blow-up solutions have prescribed asymptotics.
Dedicated to Professor Vladimir Maz'ya on the occasion of his 60th birthday.
The author was supported by the Swedish Natural Science Research Council (NFR) grant M-AA/MA 10879-304. |
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Keywords: | |
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