## On Kneser-type solutions of sublinear ordinary differential equations.(English)Zbl 0696.34034

Summary: A nontrivial solution u: [a,$$+\infty [\to {\mathbb{R}}$$ of an ordinary differential equation of n-th order is called a Kneser-type solution (KS) if $$(-1)^ iu^{(i)}(t)\geq 0$$ for $$t\geq a$$ $$(i=0,...,n-1)$$. A KS is called degenerate (singular) if it is constant (zero) in some neighbourhood of $$+\infty$$, and nondegenerate otherwise. In the paper a class of equations admitting sufficiently many singular KSs is introduced and studied. For the equations from this class a sufficient condition for the existence of a nondegenerate KS with a prescribed limit at $$+\infty$$ is established. Two-sided a priori asymptotic estimates of such solutions are obtained.

### MSC:

 34C99 Qualitative theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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