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(2001 / vol.4 / no.2)
A classification of radial self-similar solutions of the heat equation
Zheng Guo Jin, Minkyu Kwak
Pages. 45-50     



In this note we investigate some properties of solutions of ordinary differential equations $$aligned u'' +( frac r 2 + frac {N-1} r ) u' + frac 1{p-1} u&+ k|u|^{p-1} u =0, quad r>0 u'(0)&=0 u(0)&= alpha. endaligned $$ Here $k=1$ or $-1$. We explain some recent results and what should be done sooner or later.



semilinear elliptic equation, existence and uniqueness, self-similar solution



35J25, 35K15