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On Kneser problem for differential equations of the 3rd order. (English) Zbl 0696.34014
Summary: Sufficient conditions are found for the existence of a solution u of the third order nonlinear differential equation, satisfying u(t)$$\geq 0$$, $$u'(t)\leq 0$$, $$u''(t)\geq 0$$ for $$t\in [0,\infty)$$ and $$\phi (u(0),u'(0),u''(0))=0$$, where $$\phi$$ is a continuous function.
##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34C11 Growth and boundedness of solutions to ordinary differential equations