Abstract
The equation x(n)(t)=(−1)n│x(t)│k with k>1 is considered. In the case n≦4 it is proved that solutions defined in a neighbourhood of infinity coincide with C(t−t0)−n/(k−1), where C is a constant depending only on n and k. In the general case such solutions are Kneser solutions and can be estimated from above and below by a constant times (t−t0)−n/(k−1). It is shown that they do not necessarily coincide with C(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.
Funding Statement
The author was supported by the Swedish Natural Science Research Council (NFR) grant M-AA/MA 10879-304.
Dedication
Dedicated to Professor Vladimir Maz'ya on the occasion of his 60th birthday.
Citation
Vladimir A. Kozlov. "On Kneser solutions of higher order nonlinear ordinary differential equations." Ark. Mat. 37 (2) 305 - 322, October 1999. https://doi.org/10.1007/BF02412217
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