Asymptotic Behavior of Singular Solutions of Emden-Fowler Type Equations

Аннотация

We study the behavior of singular solutions of the Emden-Fowler type equation y(ⁿ) = p(x, y, y’,..., y(^n-1)|y|^k sgn y, n > 2, with a regular (k > 1) or singular (0 < k < 1) nonlinearity. A singular solution is a solution that has a vertical (possibly, resonance) asymptote (for k > 1) or a solution that vanishes together with derivatives of order < n at some point or has a point of accumulation of zeros (for 0 < k < 1).