Atypicality of power-law solutions to Emden-Fowler type higher order equations

For higher-order Emden-Fowler type equations, conditions on the roots of a certain polynomial related to the equation are obtained that are sufficient to ensure that asymptotically power-law solutions are atypical. Atypicality means that the set of initial data generating such solutions has measure zero. By using those conditions, atypicality of the asymptotically power-law solutions is proved for the equations of order $ 12$ to $ 203$ with sufficiently strong nonlinearity. A review of results is given for the asymptotically power-law behavior of blow-up solutions.