Geodesic
Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a~multiplicative one-parameter group
Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 107-127

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We study solutions to partial differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter transformation group such that all eigenvalues of the infinitesimal matrix are positive. The infinitesimal matrix may contain a nilpotent part. In the asymptotic scale of regularly varying functions, we find conditions under which such differential equations have asymptotically homogeneous solutions in the critical case. 
@article{TRSPY_2014_285_a7,
     author = {Yu. N. Drozhzhinov and B. I. Zavialov},
     title = {Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a~multiplicative one-parameter group},
     journal = {Informatics and Automation},
     pages = {107--127},
     publisher = {mathdoc},
     volume = {285},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a7/}
}
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Yu. N. Drozhzhinov; B. I. Zavialov. Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a~multiplicative one-parameter group. Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 107-127. http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a7/