On Kneser solutions of nonlinear third-order differential equations. (English) Zbl 0995.34025

The paper concerns the third-order differential equation \(y'''(t)+q(t)y'(t)+f(y(t))=0\) on \([0,+\infty)\). Existence and asymptotic behaviour of Kneser solutions \(y\) are investigated, which are either positive, decreasing, and convex, or negative, increasing, and concave on some \([t_y,+\infty)\). A typical hypothesis states that the second-order auxiliary equation \(y''(t)+q(t)y(t)=0\) is nonoscillatory.


34C11 Growth and boundedness of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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