Asymptotic Behavior of Singular Solutions of Emden-Fowler Type Equations


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Abstract

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).

About the authors

I. V. Astashova

Lomonosov Moscow State University; Plekhanov Russian University of Economics

Author for correspondence.
Email: ast.diffiety@gmail.com
Russian Federation, Moscow, 119991; Moscow, 117997

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