On existence of singular solutions. (English) Zbl 1026.34012

Summary: Sufficient conditions are given under which the differential equation \[ y^{(n)}= f(t,y,\dots, y^{(n-2)})g (y^{(n-1)}) \] has a singular solution \(y:[T,\tau) \to\mathbb{R}\), \(\tau< \infty\), fulfilling \(\lim_{t \to\tau} |y^{(j)}(t) |=\infty\), \(j=0,1,\dots,n-1\).


34A34 Nonlinear ordinary differential equations and systems
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